Jon Daly netted from the penalty spot 10 minutes into the second half, after Liam Kelly was dismissed for a last-man challenge on Gary Mackay-Steven.
Paul Dixon blasted in a superb 30-yard effort to double the hosts' lead and John Rankin then slammed home their third after 70 minutes.
With six minutes remaining Scott Robertson capped an excellent display by firing beyond Cammy Bell to add gloss to a superb evening for the Tannadice side.
Daly passed up a glorious opportunity to open the scoring with the first chance of the game after five minutes.
Johnny Russell combined with Robertson who slipped the ball inside to the striker, but his effort sailed well over.
Michael Nelson had to be alert to deal with Rankin's cross as the home side pushed for an opener and Kilmarnock responded by forcing two corners at the other end.
Lewis Toshney infuriated the home support with a late lunge on Paul Dixon and referee Craig Thomson brandished a yellow card after initially allowing play to go on.
Bell comfortably gathered from Russell after the Kilmarnock defence failed to deal with Robbie Neilson's long throw just after the 20-minute mark and the winger then fizzed an effort wide five minutes later.
Russell continued to be the heart of every United attack and he should have done better when he met Dixon's cross at the front post after 30 minutes.
The home side almost took the lead in controversial fashion as Rankin's free-kick, which was intended to be sportingly returned to Bell, looped just over the bar.
Kelly headed over as Kilmarnock created their first chance of the first half, however it was their opponents that continued to look the more likely.
He was then involved at the other end as he diverted Mackay-Steven's shot out for a corner and Daly blazed over on the stroke of half time when a pass to Russell was perhaps a better option.
United made a lightning fast start to the second half and Bell produced a wonderful stop to deny Rankin in the opening minute.
The former Hibernian midfielder came close again from the resulting corner as he forced Bell to push away his fizzing strike from the edge of the area and Robertson could not quite adjust himself to head home the rebound.
Russell was next to work Bell and the Scotland international did well to block at the winger's feet after good work by Flood on 50 minutes.
United were handed the perfect opportunity to open the score five minutes later when Thomson pointed to the spot after Kelly upended Mackay-Steven inside the area after he latched on to Daly's flick-on.
Kelly also received his marching orders after Thomson deemed that the defender was the last man.
Daly stepped up to take the resulting kick and despite diving the right way, the keeper could not keep the ball out.
The home side doubled their advantage just before the hour mark when Dixon's stunning long-range drive left Bell with no chance.
Dixon struck the base of the post as United looked to put the game beyond the reach of their opponents and they eventually stretched their lead to three with 20 minutes remaining.
Bell's punch from Flood's corner broke to John Rankin and the midfielder slammed the ball high into the net.
Nelson failed to trouble Dusan Pernis with a close-range header as the visitors tested the United keeper for the first time in the match.
It was the hosts who continued to threaten to add to their tally though and Mackay-Steven should have done better when he found himself clean through on goal.
With his side cruising, Peter Houston also made full use of his substitutes and Stuart Armstrong, Richie Ryan and Milos Lacny were all given opportunities.
Armstrong was involved in the lead-up to United's fourth goal, chipping a sublime through-pass to Robertson and he made no mistake in firing low beyond Bell.
