Dundee United finished with eight men as Rangers secured a victory that stretches their lead over Celtic in the Scottish Premier League to four points.
Mihael Kovacevic went off for fouling Steven Naismith, leading to Steven Whittaker's 22nd-minute spot kick.
Sean Dillon's red card for tripping Nikica Jelavic on the hour led to Whittaker's second successful penalty.
Fine Jelavic and Kyle Lafferty strikes bookended a missed Whittaker penalty after Morgaro Gomis' red card.
The victory not only avenged United's recent 3-2 win at Ibrox but made it five wins in a row for Rangers since that stumble for the reigning champions.
And, in defeating a side who had lost only one of their last 10 league games, they overcame a potential banana skin to put pressure on a Celtic side who have two games in hand but face a difficult trip of their own to Kilmarnock on Wednesday.
Rangers manager Walter Smith had made three changes as he attempted to improve on their unconvincing performance in beating St Mirren at the weekend.
Jelavic and Whittaker both scored against Dundee United
Madjid Bougherra returned from injury and started along with Kyle Hutton and Naismith, who was now free from suspension, with El Hadji Diouf, Jamie Ness and Richard Foster dropping out.
United handed Kovacevic his first start of the season after a long spell out through injury in place of the suspended Paul Dixon in defence.
David and Scott Robertson were recalled to midfield, with Craig Conway and Prince Buaben dropping to the bench.
Both sides were playing open, attacking football without threatening either goalkeeper until Naismith had the ball in the United net after 16 minutes.
However, the forward was pulled up and booked by referee Willie Collum for using his arm to control Garry Kenneth's headed clearance before slotting it low into the corner past goalkeeper Dusan Pernis.
Collum, though, erred in Naismith's favour moments later when Pernis could only block a powerful drive from Lafferty back across his goal and the Scotland striker was first to the loose ball only to be sent tumbling by Kovacevic's challenge from behind.
With the Swiss defender shown a red card for preventing Naismith's goalscoring opportunity, Whittaker dispatched his fifth penalty of the campaign into the corner.
United boss Peter Houston immediately hauled off captain David Robertson to bolster his depleted defence with Barry Douglas.
The re-structured back-line was almost instantly breached when Jelavic could not react quickly enough to direct Naismith's mis-hit shot from a low Davis cross inside the far post.
Rangers also made a change when Hutton was withdrawn after only 34 minutes, perhaps to avoid a second yellow card, with Diouf his replacement.
Pernis made a smart save from a Naismith header, but Rangers were playing a cagey game despite having a man advantage and United's Kenneth had a chance at the back post but miscued his volley.
Lafferty managed a better connection from a Diouf cross at the other end, but Pernis turned the 16-yard effort over the crossbar.
Dillon cleared from in front of the United goal after Naismith finished a fine run with a dangerous low cross as Rangers opened the second half on the front foot.
A Diouf free-kick found Jelavic unmarked 12 yards out, but the striker headed well over and minutes later sliced well wide after controlling the ball well on his chest from even closer range.
The mounting pressure told when Douglas was short with a pass and, when Diouf found Jelavic in space, Dillon hauled down the striker.
It looked like the offence might have been marginally outside the penalty box, but there was no doubt about the defender being the last man, or Whittaker's copycat finish from the spot.
Jelavic pounced to score from a difficult angle after the flying Pernis did well to save from a 25-yard Davis drive and the goalkeeper did well to prevent Douglas diverting the ball into his own net.
United were down to eight men when Gomis nudged Diouf in the six-yard box after 78 minutes, but Whittaker blazed over his chance to score a hat-trick of penalties.
However, Lafferty's low drive from 10 yards beat Pernis at his near post via deflection five minutes later.
There was still time for Pernis to prevent substitute David Healy adding a fifth from a powerful free kick.
Live text and stats
Tuesday, 19 April 2011
Whittaker (pen) 22
Whittaker (pen) 60
02 Dillon red card
12 Robertson (Douglas 24)
14 Swanson (Buaben 65)
16 Gomis red card
19 Kovacevic red card
25 Goodwillie (van der Meulen 62 yellow card)
21 van der Meulen,
14 Naismith yellow card (Fleck 62)
18 Jelavic (Healy 79)
41 Hutton yellow card (Diouf 34)
Ref: CollumAtt: 11,626
Attempts on target
Attempts off target
90:00+2:45 The game is over, as the referee blows his whistle.
90:00+2:06 El-Hadji Diouf decides to take the corner short.
90:00+1:03 Free kick awarded for an unfair challenge on David Healy by Scott Robertson. Free kick crossed by David Healy.
88:02 Effort from just outside the box by Steven Davis goes over the bar.
87:31 Short corner worked by El-Hadji Diouf.
83:46 Timothy van der Meulen concedes a free kick for a foul on Sasa Papac.
83:32 Free kick taken by David Weir.
83:32 Booking Timothy van der Meulen is cautioned.
82:04 Assist on the goal came from Steven Whittaker.
82:04 GOAL - Kyle Lafferty:Dundee Utd 0 - 4 Rangers Kyle Lafferty finds the back of the net with a goal from just outside the box to the bottom right corner of the goal. Dundee
Utd 0-4 Rangers.
79:55 The offside flag is raised against David Healy. Dusan Pernis takes the free kick.
78:43 Substitution Nikica Jelavic goes off and David Healy comes on.
77:27 Power penalty missed by Steven Whittaker.
77:27 Sent off Morgaro Gomis sent off.
77:08 Unfair challenge on El-Hadji Diouf by Morgaro Gomis results in a Penalty.
76:12 Corner taken by El-Hadji Diouf from the left by-line, Prince Buaben makes a clearance.
73:53 Inswinging corner taken from the right by-line by Barry Douglas, save by Allan McGregor.
73:05 Shot by Nikica Jelavic from just outside the area goes over the net.
71:17 GOAL - Nikica Jelavic:Dundee Utd 0 - 3 Rangers Nikica Jelavic grabs a goal from close in to the bottom left corner of the goal. Dundee Utd 0-3 Rangers.
69:29 El-Hadji Diouf decides to take a short corner.
66:50 Foul by John Fleck on Johnny Russell, free kick awarded. Barry Douglas restarts play with the free kick.
64:04 Free kick taken by Dusan Pernis.
64:04 Substitution (Dundee Utd) makes a substitution, with Prince Buaben coming on for Daniel Swanson.
64:04 Maurice Edu is adjudged to have handled the ball.
61:11 Barry Douglas takes the direct free kick.
61:11 Substitution (Dundee Utd) makes a substitution, with Timothy van der Meulen coming on for David Goodwillie.
61:11 Substitution John Fleck on for Steven Naismith.
61:11 The referee gives a free kick against Steven Davis for handball.
59:56 GOAL - Steven Whittaker:Dundee Utd 0 - 2 Rangers Penalty taken right-footed by Steven Whittaker and scored. Dundee Utd 0-2 Rangers.
58:37 Sent off The referee sends off Sean Dillon for serious foul play.
58:32 Penalty awarded for a foul by Sean Dillon on Nikica Jelavic.
56:21 Outswinging corner taken right-footed by El-Hadji Diouf from the right by-line to the near post, Sean Dillon manages to make
54:52 Effort on goal by Nikica Jelavic from deep inside the area goes harmlessly over the bar.
Correction - 51:14 David Goodwillie concedes a free kick for a foul on Madjid Bougherra. Allan McGregor restarts play with the free kick.
51:14 Unfair challenge on Madjid Bougherra by David Goodwillie results in a free kick. Free kick taken by Allan McGregor.
50:53 Madjid Bougherra gives away a free kick for an unfair challenge on Dusan Pernis. Free kick taken by Dusan Pernis.
50:23 Free kick awarded for a foul by Daniel Swanson on Steven Whittaker. Steven Whittaker crosses the ball in from the free kick.
48:55 Foul by Scott Robertson on Steven Naismith, free kick awarded. El-Hadji Diouf sends in a cross, Header from deep inside the
area by Nikica Jelavic goes over the bar.
47:27 Free kick awarded for a foul by Steven Naismith on Scott Severin. Dusan Pernis takes the free kick.
45:01 The referee gets the second half underway.
45:00+2:03 The ref blows to signal half-time.
45:00+1:03 Unfair challenge on Barry Douglas by Maurice Edu results in a free kick. Free kick crossed right-footed by Barry Douglas.
45:00+0:03 El-Hadji Diouf takes the inswinging corner, Header by Madjid Bougherra from deep inside the penalty area misses to the right
of the target.
44:46 Kyle Lafferty takes a shot. Dusan Pernis makes a save.
42:35 Maurice Edu concedes a free kick for a foul on Barry Douglas. Barry Douglas produces a shot on goal direct from the free kick.
42:00 Steven Naismith takes a shot. Save by Dusan Pernis.
39:10 Morgaro Gomis challenges Maurice Edu unfairly and gives away a free kick. Maurice Edu takes the free kick.
38:37 Free kick awarded for a foul by Scott Severin on El-Hadji Diouf. David Weir takes the direct free kick.
37:56 Free kick awarded for a foul by Maurice Edu on Daniel Swanson. Free kick crossed by Barry Douglas, Maurice Edu manages to
make a clearance.
37:16 Foul by Garry Kenneth on El-Hadji Diouf, free kick awarded. Sasa Papac takes the free kick.
36:06 Daniel Swanson challenges Steven Whittaker unfairly and gives away a free kick. Direct free kick taken by Allan McGregor.
34:21 Foul by Kyle Lafferty on Garry Kenneth, free kick awarded. Direct free kick taken by Garry Kenneth.
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