A last-minute goal from Gary Wales allowed Kilmarnock to move into fourth place in the SPL.
Killie took the lead after 38 minutes when Gary McDonald's attempted cross swerved into the net.
Colin Samuel pounced for the equaliser on 51 minutes, after David McCracken's header was pushed out by Alan Combe.
However, Wales showed terrific technique to fire home inside a crowded penalty box with just seconds remaining in normal time.
Kilmarnock had every reason to feel confident against a side that had only won twice away from home this season.
The first opportunity of the game fell to Killie's Colin Nish, who was handed the first chance to fill the boots of Rangers-bound Kris Boyd.
The former Dunfermline striker collected a hopeful Garry Hay clip into the box but pulled his shot wide of Derek Stillie's left-hand post in the fourth minute.
Five minutes later, Killie had an even better chance to take the lead when Steven Naismith drifted beyond a static United defence before a heavy touch allowed Stillie to smother his effort wide.
The first threat from the visitors - who recalled Stuart Duff and Lee Miller in place of the injured Peter Canero and Grant Brebner - arrived in the 33rd minute, a swift counter-attack culminating in Barry Robson narrowly failing to apply a decisive touch to Mark Wilson's astute pass.
Four minutes later the home side got the breakthrough their domination deserved when McDonald attempted to cross to the back post but cut across the ball which resulted in it swerving into the top left-hand corner of the net.
Having been witless for the duration of the first half, the Tangerines somehow mustered an equaliser just six minutes after the interval.
From Barry Robson's left-wing corner, a firm header from McCracken was pushed out by Combe but Samuel was there to fire home his third goal in four games.
Realising the need for some additional impetus Jim Jefferies threw on another striker in Wales.
It did not have the desired effect though as both sides continued to labour for the winner, a weak Lee Miller free-kick being the best United could offer.
It seemed to energise his team-mates though, as Alan Archibald threatened with a couple of half-chances either side of the 85th minute mark.
With just over 30 seconds of normal time remaining, Wales pounced on a loose ball in the box to fire low past Stillie into the bottom right-hand corner and seal the points for the Ayrshire side.
Goals: McDonald 38, Wales 90.
Dundee Utd: Stillie, Wilson, Archibald, McCracken, Ritchie, Duff, Kerr, Robson, Samuel, McIntyre, Miller. Subs Not Used: McInnes, Kenneth, Fernandez, Robertson, Cameron, Goodwillie, Samson.
Booked: Archibald, Stillie.
Goals: Samuel 51.
Att: 5,749
Ref: E Smith