Profligacy in front of goal and a controversial offside decision mean that Partick Thistle have slipped out of the top six as the Premiership goes into hibernation for four weeks.
The Maryhill side dominated for long spells as they sought a third successive league win to end the old year on a high. However, they missed good chances even if Kris Doolan was harshly flagged offside 14 minutes into the second half.
Doolan, who had been correctly ruled offside when knocking home Stevie Lawless’s pass in the second minute, thought he would celebrate his 300th club appearance with a winning goal.
It was Lawless who supplied the cross in 59 minutes and Doolan seemed to come from behind Gary Dicker to head past Jamie MacDonald but the flag was raised by Andrew McWilliam and referee Kevin Clancy chalked the goal off.
Manager Alan Archibald said: “I have not seen the goals that were ruled out again. I thought the first one was definitely offside but I thought the second one was on line.
“But, some you get and some you don’t. It is very close to be fair.
“I thought we looked tired in the second half. We have had five games in 15 days and the conditions didn’t help us.
“But, we are delighted where we are because we were bottom just over a week ago.”
MacDonald made an excellent save from Doolan five minutes before half-time after some wonderful creative play by Lawless, and Chris Erskine was horrified to see his rebound deflected wide.
However, in fairness to Kilmarnock, who were severely depleted, they grew into the game in the second half.
Charlie Adams’ diagonal ball to the back post in 67 minutes was hit back across goal by Coulibaly and from only two yards out the Albanian striker shot over the bar as he stretched.
It was a massive let-off and it gave Killie renewed belief that they might just snatch an unlikely win.
With six minutes remaining Bojaj’s shot was deflected for a corner. Jordan Jones whipped the ball over and Coulibaly was unmarked but headed wide of the right post.
Manager Lee Clark said: “We were very depleted and I had to throw in young boys
“A point away from home is never a bad result so we are relatively pleased, especially as we achieved a clean sheet.”