Keith Watson, Stuart Armstrong, Ryan Gauld and David Goodwillie all found the back of the net at a wet and windy Rugby Park where Reuben Gabriel was sent-off midway through the first half.
With an hour played, Watson broke the deadlock with a rising shot from close range thanks to Gary Mackay-Steven's assist.
United added a second on 74 when Armstrong found the bottom right-hand corner from eight yards.
Two minutes later Gauld made it 3-0 rolling the ball into an empty net after keeper Craig Samson had blocked Armstrong's initial shot before Kris Boyd headed a late consolation for the hosts from Rory McKeown's cross.
However, there was still time for Goodwillie to make it 21 goals in the last five matches for United in the first minute of injury time.
Earlier, Kilmarnock had suffered a major set-back in the 23rd minute when Gabriel left the action after collecting his second yellow card from referee Euan Norris for a brace of tackles on Armstrong.
In a goalless opening 45 minutes, Brian Graham conjured up the first shot of the game when his 12-yard effort was saved by Samson.
The same player missed again, after half-an-hour, when he headed narrowly off target from inside the box while Gauld also had a brace of strikes for the visitors.
But the game sprung to life after the break, with five goals in the final half-an-hour, to leave Kilmarnock with just one win over United in their last 17 meetings.