The visitors gave their hosts a lesson in finishing with two shots on target bringing two goals.
It was a frustrating afternoon for the home side whose inability to finish must be a concern for Craig Levein.
Meanwhile, his counterpart Jim Jefferies would have been delighted to see his revitalised team top the League and clock up their fourth consecutive game without conceding a goal.
It could have been different however as United had almost grabbed the lead in the second minute courtesy of a 25-yard volley from Garry Kenneth. Latching onto a defensive clearance, the big defender smacked it with a force that it thundered off the underside of the bar as Alan Combe watched on.
With the Tangerines in the ascendancy playing the more attacking formation, the balls continued to fly in and around the Killie box, but despite their possession, the hosts were frustrated by a combination of a strong defensive wall and their own lack of a cutting edge.
It really took the Terrors to the half-hour mark before they created another great opportunity. This time, after an excellent six-man move, Morgaro Gomis fed the ball through to Warren Feeney who dragged it to his right, but fired narrowly wide across the face of the goal past the outstretched arms of Combe.
However, against the run of play, the visitors grabbed the lead in the 40th minute with a goal, combining excellent play with woeful defending. David Fernandez took a short corner to Mehdi Taouil. Unmarked, he passed it back to the ex-Tangerine who flicked in a cross for Gavin Skelton to catch Lee Wilkie sleeping and nick a fine header high into the net.
Seven minutes into the second period and Killie again on the back foot, United almost pulled back the equaliser when Wilkie outjumped keeper Combe and as the ball broke to Francisco Sandaza, his shot was blocked on the line by three Killie defenders.
But United were thwarted again when Killie wrapped up the game with another go on the break in the 59th minute.
It was a goal which came from a combination of the United back line sleeping mixed with superb play from Taouil.
The Moroccan midfielder, who had been fantastic throughout, danced past three United players before his quick one-two fed the unmarked Danny Invincibile, who tucked the ball away superbly past the advancing Lukasz Zaluska.