Odhiambo (centre) scored after 81 minutes against Rangers at Ibrox
Eric Odhiambo's late equaliser ensured that Rangers failed to create their best start to a league season for 112 years with 10 wins out of 10.
Maurice Edu half-volleyed home from 16 yards as the Scottish champions looked like restoring their three-point lead.
A superb Allan McGregor save denied Richie Foran a second-half equaliser.
Ryan Esson denied John Fleck at the other end, but Odhiambo fired in after 81 minutes to preserve Caley Thistle's unbeaten away record since November.
Something had to give at Ibrox, where Rangers were looking for that historic tenth straight win to restore their Scottish Premier League lead over a Celtic side who had earlier defeated St Johnstone 3-0.
Edu broke the deadlock before being taken off injured
Inverness were protecting a record that has now added five games to a run started before their promotion from Division One.
Despite what was at stake in terms of history, Rangers manager Walter Smith rested Steven Naismith and Steven Whittaker ahead of the Champions League trip to Valencia.
Showing five changes, Smith's team was along more familiar lines from the youthful one that beat Motherwell to move into the Co-operative Insurance Cup semi-final in midweek.
But it was an Inverness side showing just one change from their league win over Kilmarnock last weekend, with Kevin McCann replacing Odhiambo, who started the more brightly.
Rangers burst to life after 11 minutes, with the breakthrough coming after Edu had made a mess of his first attempt to control the ball, but it sat up nicely for the midfielder to find the net with his half-volley from 16 yards.
Kenny Miller fired straight at goalkeeper Ryan Esson after a mazy run, while David Weir and Lee McCulloch both headed just wide as Rangers took firm control.
Edu, who had been struggling after a strong Foran challenge, and Weiss were withdrawn at half time, with Naismith and John Fleck, who was making his first appearance of the season following injury, entering the fray.
As Rangers adjusted, Caley Thistle went close to a surprise equaliser.
Referee Ian Brines waved away claims for a penalty after Weir challenged Foran and, seconds later, Nick Ross ought to have done better than volley wide.
Steven Davis sent a drive just wide as Rangers responded, but the Glasgow side had McGregor to thank for staying ahead moments later.
The Scotland goalkeeper somehow managed to scoop Foran's downward header over the crossbar and the forward somehow fired wide after making space for himself from the corner.
It was Esson's turn for heroics seconds later when he turned a Fleck effort out for a corner.
Rangers looked like seeing the match out until Kirk Broadfoot lost possession and Foran rolled the ball into the path of substitute Odhiambo to score.
Jonny Hayes missed a couple of chances for Inverness, while Kyle Lafferty went close at the other end as the game reached a thrilling finale.
It means that Rangers fell short in their aim of winning their opening 10 fixtures - last achieved in 1898/99, when the Ibrox side won all 18 of their league fixtures with William Wilton in charge.
The draw also means that their lead is now only one point from Old Firm rivals Celtic.
Live text and stats
Saturday, 30 October 2010
03 Weir yellow card
06 McCulloch yellow card
07 Edu (Naismith 45)
20 Weiss (Fleck 45)
14 Munro yellow card
19 Ross (Odhiambo 72)
09 Foran yellow card
10 Rooney (Sutherland 90+3)
Ref: BrinesAtt: 43,697
Attempts on target
Attempts off target
90:00+3:51 The match has reached full-time.
90:00+2:32 Substitution (Inverness CT) makes a substitution, with Shane Sutherland coming on for Adam Rooney.
90:00+2:03 Corner taken short by Steven Davis.
90:00+1:42 Inswinging corner taken left-footed by John Fleck, Grant Munro manages to make a clearance.
90:00+1:23 Inswinging corner taken from the right by-line by John Fleck, clearance by Ross Tokely.
90:00+0:08 Inswinging corner taken right-footed by Steven Davis from the left by-line.
89:53 Kyle Lafferty takes a shot. Blocked by Ross Tokely.
89:10 Close range effort by Jonathan Hayes goes wide of the left-hand post.
88:55 The ball is sent over by Kirk Broadfoot, clearance made by Ross Tokely.
88:26 The referee blows for offside. Free kick taken by Allan McGregor.
87:59 Steven Davis delivers the ball, Madjid Bougherra takes a shot. Save made by Ryan Esson.
86:13 Steven Davis challenges Jonathan Hayes unfairly and gives away a free kick. Shot comes in from Jonathan Hayes from the free
85:53 Madjid Bougherra crosses the ball, save by Ryan Esson.
83:51 Sasa Papac produces a cross, Ryan Esson fouled by David Weir, the ref awards a free kick. Free kick taken by Grant Munro.
83:51 Booking David Weir goes into the book.
83:05 Adam Rooney concedes a free kick for a foul on Steven Naismith. John Fleck delivers the ball from the free kick left-footed
from right wing, clearance made by Grant Munro.
80:57 Richie Foran provided the assist for the goal.
80:57 GOAL - Eric Odhiambo:Rangers 1 - 1 Inverness CT Eric Odhiambo scores a goal from close in to the bottom left corner of the goal. Rangers 1-1 Inverness CT.
80:10 Corner taken left-footed by John Fleck to the near post, Headed effort from close range by Kenny Miller goes wide left of
79:58 Kenny Miller takes a shot. Blocked by Grant Munro.
79:53 Centre by John Fleck.
78:21 Eric Odhiambo concedes a free kick for a foul on Madjid Bougherra. The free kick is swung in left-footed by John Fleck, clearance
by Richie Foran.
77:07 Inswinging corner taken by John Fleck from the right by-line played to the near post, Russell Duncan manages to make a clearance.
76:57 Lee McCulloch takes a shot. Blocked by Grant Munro.
75:11 Free kick awarded for a foul by Lee McCulloch on Richie Foran. Free kick taken by Grant Munro.
75:11 Booking Lee McCulloch is given a yellow card.
73:35 The ball is crossed by Kevin McCann, Kirk Broadfoot makes a clearance.
73:15 Free kick awarded for an unfair challenge on Stuart Duff by Lee McCulloch. The free kick is swung in left-footed by Grant
Munro, clearance by Lee McCulloch.
Correction - 71:58 Substitution Nick Ross goes off and Eric Odhiambo comes on.
71:58 Substitution Eric Odhiambo replaces Nick Ross.
71:43 Kirk Broadfoot sends in a cross, Effort from deep inside the area by Steven Davis clears the bar.
70:36 Russell Duncan fouled by Kenny Miller, the ref awards a free kick. Ryan Esson takes the free kick.
69:22 Unfair challenge on Kenny Miller by Grant Munro results in a free kick. Direct strike on goal from the free kick comes in
from Kyle Lafferty.
69:22 Booking Grant Munro is given a yellow card.
68:28 Steven Naismith delivers the ball, Ross Tokely manages to make a clearance.
66:54 Effort on goal by John Fleck from outside the area goes harmlessly over the bar.
65:44 The ball is sent over by Kirk Broadfoot, Grant Munro manages to make a clearance.
65:10 The ball is swung over by Graeme Shinnie, save by Allan McGregor.
64:44 Kyle Lafferty takes a shot. Ryan Esson makes a save.
64:12 Handball by John Fleck. Direct free kick taken by Russell Duncan.
62:53 Kevin McCann concedes a free kick for a foul on John Fleck. Sasa Papac takes the direct free kick.
62:14 Kyle Lafferty takes a shot. Save by Ryan Esson.
61:03 The ball is swung over by Jonathan Hayes.
60:24 The ball is crossed by Kirk Broadfoot, Foul by Kyle Lafferty on Ross Tokely, free kick awarded. Free kick taken by Ryan Esson.
59:54 Corner taken left-footed by John Fleck from the right by-line, Grant Munro manages to make a clearance.
59:30 John Fleck takes a shot. Save made by Ryan Esson.
58:19 Effort on goal by Richie Foran from inside the penalty box misses to the right of the target.
57:59 Stuart Duff takes a inswinging corner from the left by-line played to the near post.
57:43 Jonathan Hayes crosses the ball, Richie Foran takes a shot. Save by Allan McGregor.
56:13 Steven Davis takes a shot. Kevin McCann gets a block in.
55:55 Steven Davis takes a short corner.
54:04 Kirk Broadfoot crosses the ball, clearance by Grant Munro.
53:19 Free kick awarded for an unfair challenge on Lee McCulloch by Nick Ross. Free kick taken by Madjid Bougherra.
52:32 Handball decision goes against Kyle Lafferty. The free kick is swung in left-footed by Graeme Shinnie, clearance by Madjid
51:52 John Fleck crosses the ball.
50:52 Centre by John Fleck, clearance made by Grant Munro.
49:57 Effort from the edge of the area by Steven Davis goes wide of the right-hand upright.
48:18 Kevin McCann delivers the ball, Effort from the edge of the box by Nick Ross goes wide of the right-hand upright.
45:37 Inswinging corner taken by Jonathan Hayes from the right by-line played to the near post, clearance made by Lee McCulloch.
45:01 The game restarts for the second half.
45:00+0:57 The referee blows for half time.
45:00+0:24 Kevin McCann gives away a free kick for an unfair challenge on Kyle Lafferty. Direct free kick taken by Allan McGregor.
45:00 Substitution Maurice Edu goes off and Steven Naismith comes on.
45:00 Substitution John Fleck is brought on as a substitute for Vladimir Weiss.
44:17 Nick Ross fouled by Sasa Papac, the ref awards a free kick. Kevin McCann crosses the ball in from the free kick, Maurice Edu
makes a clearance.
41:28 Free kick awarded for a foul by Richie Foran on Lee McCulloch. Direct free kick taken by Maurice Edu.
40:32 The referee penalises Jonathan Hayes for handball. Free kick taken by Kirk Broadfoot.
39:28 Corner from the left by-line taken by Vladimir Weiss, free kick awarded for an unfair challenge on Grant Munro by Madjid Bougherra.
Direct free kick taken by Ryan Esson.
39:22 Kirk Broadfoot produces a cross, Ross Tokely makes a clearance.
38:25 Graeme Shinnie delivers the ball.
34:10 Free kick awarded for an unfair challenge on Vladimir Weiss by Ross Tokely. Shot comes in from Steven Davis from the free
32:55 Corner taken by Steven Davis, Lee McCulloch produces a header from deep inside the six-yard box which goes wide of the right-hand
32:47 The ball is crossed by Madjid Bougherra, Ross Tokely manages to make a clearance.
32:25 Kevin McCann sends in a cross, Lee McCulloch makes a clearance.
32:07 Vladimir Weiss challenges Kevin McCann unfairly and gives away a free kick. Free kick taken by Kevin McCann.
31:27 The ball is sent over by Graeme Shinnie.
31:09 Free kick awarded for a foul by Lee McCulloch on Stuart Duff. Direct free kick taken by Stuart Duff.
30:21 Kevin McCann challenges Vladimir Weiss unfairly and gives away a free kick. David Weir takes the direct free kick.
28:41 Steven Davis takes a outswinging corner from the right by-line to the near post, David Weir has a headed effort at goal from
deep inside the area missing to the right of the goal.
28:33 The ball is delivered by Kirk Broadfoot, blocked by Graeme Shinnie.
27:26 The ball is sent over by Jonathan Hayes, blocked by Madjid Bougherra.
24:21 Richie Foran gives away a free kick for an unfair challenge on Maurice Edu. Steven Davis crosses the ball in from the free
24:21 Booking Richie Foran is given a yellow card.
23:14 Sasa Papac crosses the ball, clearance by Grant Munro.
22:36 Corner taken by Vladimir Weiss from the right by-line played to the near post, Russell Duncan manages to make a clearance.
22:25 Kenny Miller takes a shot. Blocked by Russell Duncan.
21:51 A cross is delivered by Richie Foran, Adam Rooney challenges Madjid Bougherra unfairly and gives away a free kick. Allan McGregor
restarts play with the free kick.
21:30 Nick Ross delivers the ball, blocked by Madjid Bougherra.
18:23 Effort on goal by Jonathan Hayes from just outside the penalty area goes harmlessly over the target.
17:23 Centre by Jonathan Hayes, Richie Foran gives away a free kick for an unfair challenge on Madjid Bougherra. Allan McGregor
takes the direct free kick.
16:34 Kevin McCann delivers the ball, David Weir makes a clearance.
14:38 Kenny Miller takes a shot. Save by Ryan Esson.
13:34 Vladimir Weiss concedes a free kick for a foul on Russell Duncan. Ross Tokely takes the free kick.
10:52 Assist by Steven Davis.
10:52 GOAL - Maurice Edu:Rangers 1 - 0 Inverness CT A brilliant goal is scored by Maurice Edu from the edge of the area to the top right corner of the goal. Rangers 1-0 Inverness
10:04 Stuart Duff produces a cross.
9:55 Ross Tokely delivers the ball, Kirk Broadfoot manages to make a clearance.
9:16 A cross is delivered by Vladimir Weiss, blocked by Nick Ross.
8:47 Corner taken by Vladimir Weiss, save by Ryan Esson.
8:37 Vladimir Weiss takes a shot. Blocked by Grant Munro.
8:24 Short corner worked by Sasa Papac.
8:16 Centre by Madjid Bougherra, Ross Tokely manages to make a clearance.
5:38 Nick Ross gives away a free kick for an unfair challenge on Kirk Broadfoot. Direct free kick taken by Kirk Broadfoot.
2:04 The ball is sent over by Russell Duncan, clearance made by Kirk Broadfoot.
1:26 The ball is swung over by Richie Foran, Maurice Edu gets a block in.
0:00 The game begins.
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