It was a game in which the Terrors out-fought and out-thought their visitors. But it was also a game in which Walter Smith's team selection will be questioned after he left two of his main strikers on the bench.
From the outset, it was United who pressed, creating a first chance in the ninth minute with a powerful Noel Hunt header that flew just over, and it was closely followed by another glancing header from Barry Robson.
However, it took 23 minutes before either side had a shot on target with an excellent Robson strike being matched by Allan McGregor's save.
Rangers did have the ball in the net in the 26th minute, but Daniel Cousin was rightly flagged for offside.
The Tangerines deservedly took the lead in the 28th minute. A Willo Flood free-kick was watched by the Rangers defence allowing Lee Wilkie to ghost in and slot the ball past the keeper from four yards out.
Two minutes before the break the visitors almost grabbed an equaliser when Cousin got the break of the ball and passed inside for Lee McCulloch. Eight yards out and with the keeper beaten only a desperate lunge by Darren Dods saved the day.
The visitors started the second period in a more determined fashion, forcing two tremendous saves from stand-in keeper Euan McLean.
They were eventually rewarded in the 51st minute when Christian Kalvenes upended DaMarcus Beasley and Cousin easily converted the penalty.
But United were back in the lead three minutes later when Carlos Cuellar was penalised in the box for having both his arms around Jordan Robertson and Robson blasted the ball high into the net from the spot.
With the game running away from them, Rangers moved up a gear and substitute Nacho Novo was frustrated four yards out when a despairing tackle from Dods prevented the Spaniard as he pulled back the trigger.
The visitors continued to push forward in numbers but there was a moment of controversy in the 76th minute when keeper McGregor appeared to drop the ball and Kalvenes scored but he was adjudged to have fouled the keeper.
However, the shot-stopper atoned for his mistake in the last minute, when he pulled off a quite brilliant save from Prince Bauben who struck a magnificent 25-yard shot towards the top corner.