Rugby Park saw a rare goalless first half where Hearts had gone closest to scoring when Michal Pospisil was denied by Alan Combe's point blank save in the 18th minute.
Callum Elliot should have been able to profit from the rebound but his effort squirted wide.
Gary Wales had Killie's best first-half chance when he found acres of space inside the penalty box, but elected to play the ball wide rather than go for goal and the chance was lost.
The first period may have been goalless but Kilmarnock were ahead within 30 seconds of the restart.
Invincibile fed Colin Nish in the box and the striker's shot was blocked by Christophe Berra, but Invincibile had continued his run into the area and was perfectly placed to fire low past Craig Gordon.
Hearts weren't about to allow their title challenge to derail easily and Combe had to be alert to deny Pospisil before Elliot was inches away when his header bounced just the wrong side of the post.
As Hearts pressed everything forward, Killie had chances to kill the game.
Gary Wales was clean through on Gordon but snatched his shot wide, while two minutes from time Nish offered a contender for miss of the season when Wales teed him up three yards out.
The striker tried to side-foot the ball home but allowed Gordon time to recover and throw himself in front of the shot.