Thistle should have taken the lead as early as the third minute but Billy Gibson's diving header went the wrong side of the far post.
After 13 minutes Gibson had another chance and only a last-ditch tackle kept the scores level.
This changed five minutes later when Thistle took the lead when Mark Roberts latched on to a Stephen McConalogue pass and beat the Ayr defence, before calmly sending the ball past Mark McGeown into the far corner.
At this point Ayr were posing little or no threat to the Thistle goal and it was a full 40 minutes before their first real chance, when Jerome Vareille beat Scott Boyd, but his 18-yard shot shaved the crossbar and the chance was gone.
Thistle doubled their lead only two minutes into the second half when a Billy Gibson volley from 25 yards beat McGeown and went in off the post.
Ayr pulled a goal back on 55 minutes when the impressive Vareille cut the ball past four Thistle defenders to find Chris Robertson unmarked for a simple tap-in.
This goal seemed to spur Ayr and it was no surprise when they scored the equaliser on 76 minutes. Craig Conway was allowed to cut in from the line, beat two defenders and then strike a low, hard drive past the despairing Kenny Arthur and into the net.
Ayr continued to press for the winner, but in the end had to settle for a share of the points which will please them a lot more than Thistle.