A win would have allowed the Glasgow giants to wrap up the championship with another victory over Hearts at Ibrox on Sunday - but they now need Celtic to drop points against Hibernian 24 hours earlier for that to happen.
United - who are hoping to catch the Hoops for the runners-up spot - managed to hold on for a point despite seeing Mihael Kovacevic dismissed with 20 minutes to go.
Madjid Bougherra made his long-awaited return for Rangers, making his first appearance since the Old Firm derby in February, when he started ahead of teenager Danny Wilson after recovering from a hamstring problem.
That was the only change made by Walter Smith following last week's win over Aberdeen, with top goalscorer Kris Boyd again named on the bench and Kyle Lafferty starting up front with Kenny Miller.
United made six changes with boss Peter Houston keen to freshen up his side after booking their place in the Scottish Cup final at the weekend.
Jennison Myrie-Williams, Danny Cadamarteri, David Robertson, Kovacevic, Francisco Sandaza and Garry Kenneth - back from suspension - were added to the team, while Andy Webster - ineligible under the terms of his loan deal - was among those who missed out.
Rangers had the chance to pile the pressure on United with a free-kick just outside the box early on. Lafferty was hauled down by Kovacevic and Steven Davis stepped up for the set-piece only to curl it narrowly past Dusan Pernis' right-hand post.
At the other end, only the quick reflexes of Allan McGregor prevented Rangers from falling behind when he stuck out a leg to block a powerful 35-yard shot from Kenneth before Bougherra hooked to safety.
United were threatening again when Prince Buaben slipped a lovely ball through to Cadamarteri but he squandered a decent chance by rifling a shot into the side-netting.
But it was Miller who produced the best effort of the game so far with a superb dipping volley from the edge of the box that was equalled by a full-stretch Pernis who managed to tip the ball just over.
Rangers emerged for the second half determined to find the back of the net and Maurice Edu had a go with a shot from distance which fell harmlessly wide within a minute of the restart.
With no goals and 58 minutes gone, Boyd was thrown into the action in place of Steven Naismith, with Lafferty switching to wide left.
It was United who could have surged into the lead when Cadamarteri squeezed between Bougherra and Steven Whittaker only to drag his left-foot shot wide.
Sasa Papac was perhaps fortunate to stay on the park when he picked up the first booking of the game for a challenge on Myrie-Williams only to foul the same player again just seconds later.
Instead, it was United who found themselves down to 10 men with 20 minutes to go when Kovacevic was shown a straight red card by referee Brian Winters for foolishly kicking out at Lafferty.
Rangers tried to make the most of their numerical advantage and Miller stabbed wide, before Bougherra saw his attempts to lob the goalkeeper land on the roof of the net.
Boyd then found himself through on goal after pouncing on a Kenneth back-pass but Pernis raced off his line to block and deny the striker the opportunity to end his goal drought.
Substitute Nacho Novo had the ball in the back of the net in injury time but Boyd had already been flagged for offside, before Miller crashed his shot off the post.