This was a game in which the hosts should really have won but a combination of missed chances climaxed by a highly controversial decision by referee Mike McCurry ensured that the hosts ended with only one point instead of three.
The Terrors began in a more determined fashion with Stuart Duff carving out the first chance in the sixth minute, but he mishit and fired wide.
Then in the following minute, Stevie Crawford took advantage of neat footwork from Mark Kerr, but blasted over from the edge of the box.
A warning for the Tangerines came in the 11th minute when captain Gary Locke tried to lift his team, drilling in a low shot to test Bullock.
But the pressure continued towards the Killie goal. A deflected Jim McIntyre cross gave Barry Robson a great header but he directed it straight into the arms of Alan Combe.
It was all United at this point and the pressure finally paid dividends in the 16th minute, when Macintyre head flicked in Robson's cross.
Confusion reigned briefly as there was a lack of communication between the linesman and the referee whether the ball had crossed the line.
After Colin Nish had a sight of goal in the 23rd minute, in which he should have forced a save from the keeper, United continued to pour men forward. With Robson and Mark Wilson featuring heavily on the wings, both Duff and Crawford created and subsequently wasted good opportunities.
More pressure in the visitors box came as United tried to extend their lead before the break.
As they came out after the half-time team-talk, hearing scores from the other games filtering through, this seemed to cause anxiety and it spread right across the team.
Suddenly, the Ayrshire men lifted their spirits and their level of play, eventually stunning the Terrors with a 52nd minute equaliser.
Sub Kris Boyd, who has a tremendous record of scoring against United, took advantage of a slip from the keeper to ram the ball home from five yards.
Bullock appeared to be static when Gordon Greer's header gently passed him by and rebounded off the post for the wantaway striker to pounce.
The Tangerines lifted themselves and after missing four clear chances, they felt even more aggrieved ten minutes form time when Robson was clearly pushed to the ground in the box, but somehow the official waved the claim away.
Despite this, they continued to produce the chances and could only blame themselves for not taking maximum points.