Killie striker Kris Boyd stole the show after scoring five goals in an amazing game at Rugby Park.
Kris Boyd wheels away after scoring his hat-trick
The young Killie striker got his first after seven minutes with a 25-yard strike, then bagged his second ten minutes later with a close-range shot.
Alan Archibald pulled one back but Boyd drove in a third and grabbed a fourth with a 37th minute penalty.
Billy Dodds scored a late consolation before Boyd buried a close-range fifth to cap a stunning afternoon.
Killie took the lead with only seven minutes gone, Boyd pouncing on a mis-kick by United keeper Hirschfeld and gleefully slamming the ball into an open goal from 25 yards out.
Ten minutes later, Boyd bagged his second, knocking home with his left-foot from close range following good work on the right wing by Johnston and Dargo.
The visitor's hauled themselves back into the match in the 29th minute after defender Alan Archibald scored his second goal of the season with a six-yard header from a Barry Robson corner.
Boyd earned his hat-trick in the 32nd minute, lashing a low left-footed shot past Hirschfeld from a Peter Leven pass.
Christmas came early for the Killie youngster as he was called upon to score his fourth from the penalty spot in the 37th minute after fellow striker Danny Invincibile was tripped in the box by Archibald.
Unbelievably, Boyd found the net for a fifth time in the 40th minute from a Johnston corner - but referee Toner chalked off the strike after an earlier infringement.
After the break, substitute Billy Dodds kept United in it with a 78th minute shot after latching onto a Stewart Duff pass at the edge of the box.
But Boyd capped a sensational solo performance when he grabbed his fifth with six minutes left following good work from Invincibile down the right flank.
Kilmarnock: Combe, Lilley, Dindeleux, Greer, Leven, McDonald,
Dillon, Johnston, Invincibile, Boyd, Dargo. Subs: Smith, Fowler,
Wales, Murray, Dodds, Canning, Naismith.
Dundee Utd: Hirschfeld, Duff, Innes, Archibald, McCracken,
McInnes, Wilson, Brebner, Robson, McIntyre, McLaren. Subs:
Jarvie, Dodds, Grady, Kerr, Scotland, Bell, O'Donnell.
Referee: K Toner (Scotland)