Rangers manager Paul Le Guen had to settle for a share of the points on his Ibrox debut as Dundee United put their troubles behind them for a draw.
Noel Hunt put United into a shock lead after just 15 minutes with a tremendous strike, and the Tangerines held on to the break after constant home pressure.
United's new Norwegian Christian Kalvenes powered in a header for a shock second against the run of play.
Chris Burke replied before Steven Robb's own goal gave Rangers a point.
Rangers boss le Guen kept faith with the team which won 2-1 at Motherwell last weekend for his first competitive game at home.
The Frenchman was given a rapturous welcome from a sold-out stadium, prior to kick-off.
New Slovakian striker Filip Sebo was named as a substitute, along with Kris Boyd and Chris Burke, who returned from suspension and injury respectively.
Dundee United, who slumped to an opening day home defeat by Falkirk, signed Brann Bergen defender Christian Kalvenes in midweek and he was given a start.
Player-boss Craig Brewster, meanwhile, confined himself to the dug-out.
Rangers new golakeeper, Lionel Letizi, comfortably held a shot from Noel Hunt, but, predictably, Rangers were setting the tempo.
Alan Archibald cleared youngster Charlie Adam's effort off the line after being set up by Thomas Buffel.
However, the Tangerines shocked the home support with an expertly-taken opener after 15 minutes.
Midfielder Stuart Duff crossed from the left, and Irishman Hunt held off the challenge of Karl Svensson, before swivelling to strike beautifully into the top corner.
Rangers responded with Sionko threatening, only for Stille to save from seven yards.
The Light Blues were playing attractive football, but the killer instinct was lacking.
Sionko, playing confidently, crashed a shot off the bar and Greg Cameron knocked a Julien Rodriguez header off the line, with no end of pressure being applied by Rangers.
Dado Prso, Adam, Buffel and Sionko were all left frustrated following a series of spurned chances and United held on for the interval.
Le Guen elected to replace the impressive Adam at the break with Kris Boyd, in an attempt to break the Taysider's resolve.
But Rangers hesitancy in defence was punished when Kalvenes made it two.
Barry Robson floated in a free-kick and the debutant Norwegian rose to bullet home a header, leaving Letizi with no chance.
Le Guen reacted by sending on substitute Burke for Svensson - and it was an inspired move, as a minute later the young Scot pulled a goal back.
Turning inside, Burke curled a shot from 25 yards in off Stillie's left-hand post for the perfect reply, just when the game was in danger of running away from Rangers.
New Ibrox signing Sebo replaced Prso to give him his first taste of Scottish football as Rangers continued to search for an equaliser.
But it was a mistake from Steven Robb which allowed the Glasgow side back into the game, after 79 minutes.
Robb, who had only just entered from the bench, was involved in a mix-up with Stillie, and the midfielder could only the ball into his own net after a hopeful punt forward from Stevie Smith.
It was a lifeline Rangers deserved for all their efforts.
Rangers: Letizi, Hutton, Rodriguez, Svensson (Burke 57), Smith, Hemdani, Clement, Sionko, Buffel, Adam (Kris Boyd 45), Prso (Sebo 70). Subs Not Used: McGregor, Rae, Pierre-Fanfan, Ponroy.
Goals: Burke 57, Robb 79 og.
Dundee Utd: Stillie, Kalvenes (Robb 77), McCracken, Mair, Archibald, Cameron, Duff, Kerr, Robson, Hunt (Miller 67), Samuel. Subs Not Used: McLean, Conway, Kenneth, Gardiner, Robertson.
Booked: Mair, Duff.
Goals: Hunt 15, Kalvenes 56.
Att: 50,394
Ref: D McDonald