Jon Daly got the ball rolling when he netted from the penalty spot ten minutes into the second half, after Liam Kelly was dismissed for a last-man challenge on Johnny Russell. Further Paul Dixon, John Rankin and Scott Robertson goals capped an impressive evening for the hosts.
Willo Flood returned to the United starting line-up, the former Celtic midfielder replacing Stuart Armstrong, while Kenny Shiels stuck with the same Kilmarnock side that began the shock 1-0 victory over Rangers at Ibrox on Saturday.
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 Daly. The striker only had goalkeeper Cammy Bell to beat but his effort sailed over the bar.
The first half remained goalless, United failing to convert their superior possession into goals, but they did break the deadlock on 56 minutes when referee Craig Thomson pointed to the spot after Kelly upended Russell inside the area after he latched on to Daly’s flick-on.
Kelly received his marching orders after Thomson deemed the defender to be the last man and Daly fired the resulting kick into the back of the net.
Peter Houston’s men doubled their advantage just before the hour mark when Dixon’s stunning 30-yard 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 did just that soon after when Rankin blasted home the home side’s third with 20 minutes remaining after Kilmarnock failed to deal with Flood’s corner. Bell’s punch broke to the midfielder who slammed the ball high into the net.
United continued to press and Gary Mackay-Steven should have done better when he found himself clean through on goal. But the rout was complete with five minutes left as Armstrong – on as an 80th-minute substitute – chipped a lovely through-ball to Robertson and he made no mistake in firing low beyond Bell.
Dundee United: Pernis, Neilson, Dillon, Gunning, Dixon, Flood, Robertson, Rankin, Mackay-Steven (Ryan 82), Daly (Lacny 75), Russell (Armstrong 80). Subs not used: Banks, Watson, Douglas, Dow.
Kilmarnock: Bell, Toshney, Nelson, Sissoko, Hay, Kelly, Johnson (Van Tornhout 59), Fowler, Gordon, Shiels (Dayton 74), Heffernan (Kennedy 70). Subs not used: Letheren, Kroca, Racchi, McKeown.