The Bairns should have gone ahead in the 14th minute when Steve Thomson had a free header at the far post, but he could only clip the top of the bar.
Falkirk took the lead in the 42nd minute after more good interplay on the edge of the Kilmarnock box.
Again Russell Latapy was instrumental and his short pass gave Anthony Stokes the shooting chance from 22 yards and the young loan star despatched the ball into the net via a deflection off Garry Hay.
Stokes should have scored the second within sixty seconds of the restart but Graeme Smith saved with his legs.
The visitors hit the woodwork for a second time three minutes later when Stephen O'Donnell's deflected shot smacked off the upright.
Killie skipper Hay may have felt unlucky for his part in Falkirk 's opener, but he made up in fine style when he fired in the equaliser from 20 yards in the 59th minute after Falkirk had failed to clear Peter Leven's corner.
Kilmarnock took an unlikely lead eight minutes later when O'Donnell could only head another Leven dead ball over his keeper and into his own goal.