In the first game of the post-Barry Ferguson era, Rangers were somewhat fortuitous to leave Tannadice with a victory and with a scoreline that was deceiving based on the balance of play.
United, having suffered consecutive defeats in their opening three matches, rang the changes from Tynecastle, dropping five players including Scotland's international goalkeeper, Paul Gallacher.
With Mikel Arteta taking the central midfield role, Rangers opened the first 15 minutes spraying the ball around with confidence.
It took until the 13th minute before they created the first opening. Ronald de Boer opened up the defence but Tony Bullock got back to block the attack.
The ball broke on the edge of the box to Shota Arveladze who returned it with a beautiful chip off the top of the bar, United, looking jittery in defence, were penalised in the following minute for their indecisiveness. Debutant Chris Innef tried to usher the ball out at the byline only to allow Michael Mols to steal the ball and cross for the unmarked Nuno Capucho to stroke the ball in from six yards.
After constant pressure, Rangers eased off as the half progressed and United did become more of a force without threatening Stefan Klos' goal.
Barry Robson opened the second period for United with a blistering shot that flew just over the bar following excellent footwork on the edge of the box With the forced substitution of de Boer in the 51st minute Rangers seemed to lose their way.
An excellent move by the Tangerines in the 58th minute almost brought the equaliser. Derek McInnes chipped the ball to Colin Samuel who then knocked the ball down for Charlie Miller who forced a tremendous save from Klos.
Two minutes later Klos again denied the same player as he let fly with a 20-yard drive.
Astonishingly the game continued in this vein with United attacking until the 82nd minute when ex-Rangers star Billy Dodds came on as a substitute and scored with his first touch with a headed flick from Jason Scotland's cross.
However, there was a twist two minutes later when Arveladze turned Innes and volleyed high into the net from seven yards.
Rangers were then awarded a soft penalty two minutes from time when McInnes' foul on Mols allowed Arteta to wrap up the points.