Midfielder Gavin Skelton capped his first start for the Ayrshire side since signing from Gretna with his first goal just before the interval after the hosts had dominated the first half.
A fine finish to a good move by Danny Invincibile in the 58th minute doubled the visitors' lead and although United continued to press, Killie resolutely held out for the three points that put them top of the SPL at least until the Old Firm play at Parkhead on Sunday.
The signs looked good for the Rugby Park side before the game, Jim Jefferies' men having yet to concede a goal this season and in the midst of their best defensive run in eight years.
In truth, they performed a classic first-half smash-and-grab by scoring from their first corner of the game in the 40th minute.
The impressive and tireless David Fernandez played the ball to Mehdi Taouil, who played it back to the Spaniard. And when the cross was whipped in, Skelton stole in to head past the helpless United keeper Lukasz Zaluska.
Craig Levein's troops must have sloped off at the interval wondering quite how they were behind after dominating the first period.
The Ayrshire side were nearly undone by a remarkable volley from Garry Kenneth in the second minute, the United stopper picking up a loose David Lilley header 35 yards from goal and unleashing a shot which beat Alan Combe only to rebound off the crossbar before being knocked back to the Killie keeper by Garry Hay.
That near-miss spurred United on and they bossed the early part of the game with some authority, winning several corners which were all keenly defended by the visitors.
While Killie looked to be enjoying their defensive duties, Zaluska was a mere spectator in the United goal.
Fernandez was fighting a losing battle in his lone striker's role and as the first half progressed, the corner count mounted in the Tannadice side's favour but to no avail.
United eased closer and on the half-hour mark, midfielder Morgaro Gomis turned and set Warren Feeney up inside the Killie box but the Irishman drilled his angled shot from 16 yards wide of the far post before Skelton popped up with the shock opener.
Two minutes after the break, Killie midfielder Manuel Pascali picked up his third booking in four SPL games since arriving from Parma, this one for a foul on Francisco Sandaza.
United were soon back in the ascendancy and when Combe dropped a looping Willo Flood free-kick inside his six-yard box, there was a moment of panic before the visitors cleared their lines.
The game became increasingly heated, United claiming twice for a penalty when Lee Wilkie and then Scott Robertson went down in the box as the Tannadice side peppered thir opponents' goal.
But it was Invincibile who doubled the visitors' lead with a wonderful goal in the 58th minute.
Taouil was again instrumental in the three-man move down the left-hand side, his reverse pass sending the Australian through on goal to slide the ball past Zaluska from 14 yards, leaving the Tannadice men stunned.
United kept pressing but with less conviction than earlier and all the time leaving gaps Killie promised to exploit on the counter.
David Goodwillie and Jon Daly, both on target against Cowdenbeath in midweek, were thrown on for Feeney and Sandaza as desperation replaced inspiration.
The game fizzled out as United's hope was slowly sapped by Kilmarnock's determination to keep another clean sheet.