Blustery conditions made for a forgettable first half where United spurned the only clear chance.
Killie centre-half Frazer Wright had to leave the field for attention to an eye injury and United found space for Jon Daly to run in on stranded keeper Alan Combe, but the Irishman could only hit the side netting.
The home side took the initiative immediately after the restart, after replacing the injured Grant Murray with Colin Nish, but failed to capitalise on two golden chances.
The first came form the penalty spot after debutant Rocco Quinn was brought down by Garry Kenneth, but Derek Stillie made a great save from Steven Naismith's powerful kick.
Nish then failed to capitalise on Kenneth's slip. He took the ball round the keeper but his shot blocked by Christian Kalvenes.
The opening goal did come in the 61st minute after great build-up on the left. Allan Johnston picked out Leven inside the box and the midfielder drilled a low shot into the far corner.
Killie lost another defender when Simon Ford suffered a bad head knock, but United failed to breach the makeshift defence.
Combe presented Daly with a chance to equalise in the 78th minute when he mis-hit a bouncing back pass, but the striker lacked composure and the keeper was able to recover.
Johnston almost sealed the win two minutes from time with a powerful curling effort, but Stillie threw himself to his left to tip the ball behind, but despite throwing everyone forward, United couldn't rescue a point.