With the flags viciously flapping behind, the Bhoys started in top gear with Aiden McGeady almost drawing first blood inside two two minutes as he danced past two defenders before firing just over from the edge of the box.
Apart from Warren Feeney's token 25-yard effort in the 13th minute, it was very much the Tangerines on the back foot in the opening 20 minutes as they tried to counter both the conditions and playing uphill.
But they eventually relented in the 23rd minute with a cheap goal from Scott McDonald.
Paul Hartley's corner was headed on by Feeney and with Lee Wilkie pleading he had been fouled, the little poacher nipped in to head home Lukasz Zaluska's poor clearance for his 16th goal of the season.
It took United 28 minutes to construct a move of value and it almost brought reward as a superb three-man passage of play ended with Craig Conway's low volley being brilliantly turned around the post by Artur Boruc.
However with the wind, the visitors held their advantage and in the 38th minute, Zaluska made amends with a wonderful stop from McDonald.
Two minutes later a lunging foot from Paul Dixon prevented a certain McGeady goal and from the resulting corner, Morgaro Gomis hooked Jan Vennegoor of Hesselink's header off the line.
But it was game on after 47 minutes when Franco Sandaza took advantage of some free space from Dixon's corner to glance the ball into the top corner from nine yards out.
And the game was turned on its head nine minutes later when Sandaza grabbed his second again from isolated position.
James Wesolowski sent Dixon down the right and with his weaker foot he dragged the ball across the box for the Spaniard to sweep the ball past the outstretched arms of Boruc.
With United in control, there was no shortage of chances for them to extend their lead, although the Hoops had a few opportunities to grab the equaliser.
And they did take one in the 81st minute when a cross flew off the head of Garry Kenneth and was volleyed home like a bullet by Lee Naylor from the edge of the box.