A comedy of errors inside the first five minutes allowed Rory McKenzie and Borja Perez to claim their first goals for Kilmarnock before Jude Winchester grabbed the home side's third inside 10 minutes to give Kenny Shiels' side their first win of the season.
And although Jon Daly pulled one back for the Tannadice side it did little to placate manager Peter Houston, who was raging on the touchline throughout the second half.
The afternoon had not started well for the Rugby Park side who, already without keeper Cammy Bell with a broken wrist, suffered another injury blow after only 12 minutes.
Gary Harkins went down in an aerial challenge with Gavin Gunning in the centre of the park and though the referee gave Kilmarnock advantage, resulting in Perez's shot being blocked at the edge of the box, Harkins remained grounded. After lengthy treatment to his face, the Kilmarnock player eventually left the field on a stretcher and was replaced by youngster Winchester.
The change did not affect Killie's enthusiasm and passing game and Liam Kelly was the next to see his shot from just outside the area deflected for a corner.
United gave notice of their goal threat after 20 minutes when Willo Flood picked out top scorer Daly. Unmarked and about six yards from goal, though, he lashed his shot high over the crossbar.
Perez, on his first start, was proving influential for the Rugby Park side and a sweeping move started by the Spaniard ended with his cheeky back-heel which sent the ball just wide of goal.
The potent United attack was well marshalled by the home defence but a poor clearance from Kyle Letheren provided John Rankin with the chance to cross for Daly to drive his volley across and wide of goal, much to the keeper's relief.
The Welsh-born keeper then produced the first save of the half after Johnny Russell, free from suspension after a successful appeal against his red card in last week's Dundee derby, was tripped at the edge of the box.
From the resultant free-kick, Barry Douglas curled his shot under the bar but Letheren rose to palm the ball over his crossbar and leave the sides level at the break.
The teams returned to the field to a downpour and a greasy surface but that was no excuse for United's crazy defending in an incredible opening to the second half.
Within a minute, and with no apparent danger, Douglas elected to dribble the ball across the face of his own goal. But as he hesitated for his keeper to boot the ball clear, debutant McKenzie nipped in and, from two yards, claimed the first goal of his career - unlikely ever to be surpassed as his easiest.
United's charitable mood continued and two minutes later Mackay-Steven needlessly tripped Danny Racchi just inside the box to concede a penalty. Perez capped his first start with a goal, confidently stroking the spot-kick into the corner of the net to make it 2-0.
The home side then pressed for more goals and as the visitors' defence started to crumble, it took a fabulous twisting save from Radoslaw Cierzniak to turn Winchester's deflected shot over the bar.
The Killie substitute was not to be denied his first goal though and after 55 minutes Racchi's corner into the six-yard box was not cleared, allowing Winchester to turn and lash the ball high past the keeper and virtually end the game as a contest.
Sean Dillon almost added his name to the comic error list when he slipped at the edge of the box, leaving McKenzie a run and shot at goal, but Cierzniak turned the ball wide to save his defender's blushes.
Twelve minutes from time, Douglas found Daly in space and from 10 yards he slid the ball into the corner of the net but by that stage United's self-inflicted damage was already done.
