Killie's injury woes haunted them again as they had to change their teamsheet minutes before kick off, as Mehdi Taouil broke down in the warm-up to be replaced by the rusty Allan Johnston.
Both sides were dangerous at set-pieces with wicked deliveries testing both keepers without finding an early breakthrough.
United's inspirational skipper Barry Robson gave his side the lead in the 31st minute after slack Killie defending had presented United with the ball just outside their own box. The ball was played to Robson who squeezed the ball home below the sliding Alan Combe and Frazer Wright.
Danny Invincibile and Paul di Giacomo had half-chances to equalise, but both failed to hit the target.
Another defensive mistake, this time from Wright, allowed Noel Hunt a free run at Combe, but the keeper did well to force the striker wide and the chance was gone.
Combe had to perform heroics to keep his side in the match before half-time, acrobatically denying Sean Dillon, whose header seemed destined for the top corner.
United were holding Killie with ease after the break, despite a double substitution from Jim Jefferies at half-time.
Gary Wales and Willie Gibson were introduced to breathe new life into the home attack, but it was not until the 60th minute that they looked threatening.
Invincibile, Wales and Jamie Hamill drove at the United defence, but Wales' final pass was too close to Hamill, whose shot was blocked.
United went two up four minutes later after more calamitous defending. There seemed little danger from Robson's deep cross, but Martyn Corrigan stopped expecting Combe to catch, but did not notice Combe slip, which gave Craig Conway a simple header into the empty net.
KIllie earned themselves a lifeline with eight minutes to go with their best move of the game.
They passed the ball patiently and worked it to substitute David Fernandez who teed up Wales, who made no mistake from ten yards.