It was a game in which the visitors had much of the possession but did not carry the threat their play deserved.
United, who had not beaten their rivals at home since early 2004, soaked up the pressure and hit on the break.
In a dismal opening period, the visitors really should have gone ahead with only four minutes on the clock. A brilliant through ball from captain Barry Ferguson left Nacho Novo with only the keeper to beat.
The Spaniard, who scored in the midweek European tie, elected to lob the ball over the keeper. However, his touch was too strong and it went over the top.
United, with their new manager, made seven changes to the line-up after last weeks embarrassment at Falkirk. They took 17 minutes to carve out their first chance. It was young Greg Cameron sitting at the edge of the box who got the ball from a clearance, but blasted the ball high.
As the visitors dominated without threatening, only a last-ditch booted clearance in the 27th minute from Derek Stillie prevented the onrushing Thomas Buffel from scoring.
And with the break approaching, Dado Prso skirted around Christian Kalvenes but his inviting cutback was cleared by a combination of three United defenders.
After being pressed back, the Tangerines had a couple of quick chances to grab the lead before the break. Firstly Sasa Papac almost put the ball in his own goal as he stuck a foot out at Collin Samuel's cross.
Then David Robertson's wonderful volley from the edge of the box saw a fantastic save from Allan McGregor in response.
Into the second period the visitors grabbed the lead with a goal from Charlie Adam. Latching on to Novo's low cross, the midfielder ghosted in and stroked it home from eight yards.
It could have been two five minutes later when a David McCracken stumble allowed Ferguson to put Adam through, but his goalbound chip was booted off the line by the recovering McCracken.
Gradually United edged themselves more into the game and they had a superb chance to equalise in the 66th minute, with a sweeping move and cut back from Barry Robson which Craig Conway blasted over from 12 yards when it seemed easier to score.
And after the misfiring Novo missed again, United grabbed the equaliser in the 76th minute from Garry Kenneth. This was after sustained pressure and several corners that the Under-19 international bulleted a header down and high into the net from seven yards out.
A couple of minutes later and David Goodwillie had the away support holding their breath as he dragged his shot and it drifted wide in slow motion.
But it went from bad to worse for the Gers in the 82nd minute when Conway's free-kick was met by Lee Mair at the edge of the six-yard box, as he outjumped Adam and headed the ball under the body of McGregor.