The Edinburgh side seemed to be heading for a victory which would have reinforced their position in third place in The SPL, but Invincible popped up with time running out to boost Killie's hopes of avoiding the drop.
The first half was a tense affair, with neither side able to make the breakthrough, and it was not until after the hour that the crowd had something to cheer about.
It was the visiting fans who were boosted when Andy Webster stabbed the ball home after Killie failed to clear a corner just after the hour mark.
Hearts had a couple of chances to double their advantage, but failed to turn their possession into goals and were made to pay when Invincible headed home with three minutes remaining.
