A game which Rangers should have won easily ended up with the Ibrox side hanging on desperately at times towards the end.
After goals from Nuno Capucho and Peter Lovenkrands in the opening 20 minutes, Rangers thought they could afford the luxury of Emerson's spot-kick being saved just before half time.
However, when former Gers favourite Billy Dodds reduced the deficit early in the second half Rangers became disjointed though still managing to squander chances at the other end.
Chris Burke starting his first League game this season threatened early on when he outstripped Alan Archibald only to see his strike drift wide of the far post.
His next contribution was to put Capucho through on goal, but Paul Gallacher dived bravely to block his shot.
Lovenkrands fired over a dangerous cross which Michael Mols just failed to reach before Rangers pressure finally paid off.
Fernando Ricksen's first-time pass found Capucho who held off David McCracken's challenge before curling his shot past Gallacher.
The home team soon added to this lead when Ricksen's header was well controlled by Mols, who fed Burke and the youngster's superb cross was bulleted home by Lovenkrands.
Mols had the ball in the net after a superb volley but Capucho had been ruled offside in the build-up. The Dutch striker showing a lack of confidence in front of goal then shot weakly at the keeper after Lovenkrands had yet again tricked Mark Wilson.
When the Danish winger was taken down by Mark Kerr, the initial foul looked to have taken place outside the box, but Gallacher, diving to his left, was able to turn Emerson's penalty behind.
Dodds looked to have won a stonewall penalty for the visitors after Ricksen brought him down just after the restart. The striker was then booked when his frustration boiled over with a wild lunge at Ricksen.
Mols and Lovenkrands passed up further good chances before Dodds prodded home from close range after Jim McIntyre's header from Barry Robson's corner had been cleared off the line by Stephen Hughes.
It was perhaps justice that Dodds scored after being denied a penalty, but United failed to capitalise on some late pressure though subsitute Charlie Miller volleyed in a shot which just cleared the crossbar near the end.