Stuart Duff's eighth minute header was the all important statistic at the end of the game and while Rangers manager Alex McLeish looked on in disgust his counterpart Gordon Chisholm celebrated his second major scalp in three days.
After dispatching Hibs in Saturday's Scottish Cup semi-final, United were keen to carry that form back to the SPL and their excellent record against Rangers - in the league at least - afforded them some confidence ahead of this encounter.
Rangers were woeful for much of the match but in particular in the early stages. Thus, when Duff headed Jim McIntyre's left-foot cross home at the second attempt, it came as no great surprise to the Ibrox faithful.
When the Gers hit back, Nacho Novo somehow blasted over from close range in the 15th minute, after Dado Prso had turned excellently in the box. Then, four minutes later, Prso himself was at fault when he side-footed the ball past the post when it seemed easier to score.
Novo was denied by United's in-form goalkeeper Tony Bullock just after the half-hour mark and Bullock saved from Prso and Novo again before half time.
Bullock was even better in the second half, but in the 50th minute the visitors threatened when Sotirios Kyrgiakos allowed the ball to bounce and McIntyre's lob hit the woodwork on its way over.
Novo then saw his looping header cleared off the line by Paul Ritchie and Kyrgiakos shot straight at Bullock.
Rangers saved their best efforts for the last few minutes. Shota Arveladze missed an easy chance, Prso was denied by a Bullock stop and the goalkeeper then tipped Kyrgiakos' left-foot volley from the edge of the box over for a corner.
United have now taken seven points from a possible nine from Rangers this season.