Rangers failed to take advantage of Saturday's draw between Hearts and Celtic as they were held by Dundee United at Tannadice.
The closest the reigning champions came to a goal was Barry Ferguson's first-half free kick that came back off Derek Stillie's right-hand post.
Barry Robson saw a shot cleared off the line by Julien Rodriguez late in the second half.
Rangers' Sotirios Kyrgiakos was then sent off for a second bookable offence.
The first opening presented Chris Burke with a chance to give Rangers the lead after six minutes, but the winger volleyed over the bar from just inside the box.
Francis Jeffers then saw a back-header cleared off the line by Alan Archibald with Stillie beaten.
United continued to live dangerously as Peter Lovenkrands failed to put the ball into an empty net following excellent work by Dado Prso.
Rangers were dominant in terms of possession, but United's dogged defending was proving effective.
When the home side's resolve was finally broken, the woodwork came to their rescue. Ferguson's free kick beat the wall and the goalkeeper but the ball came back off the post.
Slack play by Rangers debutant Brahim Hemdani gave United's David Fernandez an early sight of goal in the second half, but the Spaniard's tame shot trundled by the left-hand post of Ronald Waterreus.
Jim McIntyre did test Waterreus a few minutes later, but his dipping volley from outside the box was well held by the Dutchman.
United manager Gordon Chisholm had clearly urged his team to push forward more after the break and they had a glorious chance to go ahead when Robson found himself unmarked on the edge of the box, but he shot straight at Waterreus.
David McCracken was next to pass up a goalscoring opportunity as he headed straight into the keeper's arms from six yards.
Rodriguez kept the scoresheet blank with a terrific goal-line clearance from Robson's powerful shot after Waterreus had left his goal to head away from Collin Samuel.
Kyrgiakos, booked in the first half for kicking the ball away, was ordered off for a shove on Samuel in the final minute.
Dundee Utd: Stillie, McCracken, Ritchie, Archibald, Wilson, Canero, Brebner, Kerr, Robson, Fernandez (Miller 71), McIntyre (Samuel 72).
Subs Not Used: Samson, McInnes, Duff, Kenneth, Cameron.
Booked: Robson, Brebner.
Rangers: Waterreus, Ricksen, Rodriguez, Kyrgiakos, Bernard, Burke (Namouchi 62), Ferguson, Hemdani, Lovenkrands (McCormack 78), Jeffers (Nieto 53), Prso.
Subs Not Used: Klos, Andrews, Murray, Lowing.
Sent Off: Kyrgiakos (90).
Ref: C Richmond