Nadir Ciftci, Gavin Gunning and Farid El Alagui were on target for United while Jordan Forster scored for Hibernian, who also had midfielder Tom Taiwo dismissed.
United opened the scoring when Ciftci (43) used his strength to hold off Paul Hanlon to latch onto a lofted pass before stepping inside Michael Nelson and tucking the ball past Ben Williams from 12 yards.
The lead lasted just two minutes though as United goalkeeper Radoslaw Cierzniak punched an Alex Harris corner straight to Forster and the Hibs defender nodded the ball into the open goal.
Gunning restored United's lead on 56 minutes when he rose above the Hibs defence at the back post to power his header his into the net from a superb Gary Mackay-Steven corner.
Substitute El Alagui (83) sealed victory when he clipped the ball home at the front post after Mackay-Steven and Andrew Robertson combined to open up the Hibs defence on the left side of the penalty area.
In what was an almost identical incident to the Hibs goal Cierzniak came to deal with an early Harris corner and punched the ball off the head of Hanlon, but fortunately for the keeper it spun over the bar.
United then came close when Gunning rolled a free-kick to Ciftci and his drive from 25 yards spun off the advancing defensive wall and spun an inch past the post with Williams moving in the opposite direction.
The visitors were awarded a penalty when Hanlon upended Ryan Dow, although the foul appeared to take place outside the box, but justice was done when Williams got down to his left to save Ciftci's spot-kick.
And Williams had to be alert a minute later to tip Dow's curling cross over the target at his near post, before the Hibs keeper was again in action when dived across to turn Ciftci's net-bound header away for a corner.
Just after the break Ciftci cut in from the right a curled a low drive just past the far post with Williams beaten at full-stretch.
Mackay-Steven had the chance to increase the lead four minutes after Gunning's goal, when the United defender was tripped by Nelson in the box, but the winger blasted his penalty over the bar.
A miserable night for Hibs was compounded when Taiwo was booked for a second time on 72 minutes for a late challenge on Paul Paton.