Aidan Nesbitt scored Falkirk’s goal with a fine individual run and shot after seven minutes to equalise Fraser Murray’s third minute opener from a Daniel Armstrong pass.
But Killie bossed most of the rest of proceedings and progressed comfortably with second half goals from Jason Naismith and Murray’s second.
Falkirk manager Paul Sheerin said: “They came at us and started the game well.
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"We were caught in the headlights a bit and they got their goal.
"But I thought our response to losing the goal was really good and we were a bit braver on the ball and better in possession.
"I was pleased with the last 10 minutes of the first half but in the second half we lost our way a wee bit.
“They will learn from that and that is what we will use it as.
“It could have been more in the second-half and there were a few cutbacks they probably will think they should have done better with.
“We just need to dust ourselves down and go again.”
With the game poised at 1-1 after 27 minutes, Killie had a ‘goal’ disallowed as captain Euan Murray turned a cross in with his hand.
Chances were flowing at either end, with home debutant Oli Shaw having a shot deflected just wide.
It was 2-1 Kilmarnock on 54 minutes when Naismith shot home low after a fine pass by ex-Bairn Blair Alston.
Jamie Wilson had a shot blocked by the home keeper before Killie’s Liam Polworth somehow headed wide from a Fraser Murray cross.
Falkirk sub Ben Hall narrowly avoided scoring an own goal when he turned a cross just wide, before Brad Lyons missed a sitter from a Polworth pass.
After a Mackenzie Lemon mistake let in Shaw, Bairns keeper Paddy Martin rushed out to block.
But the killer third goal came on 77 minutes when the Killie keeper’s long clearance was flicked on and Fraser Murray shot in. Craig McGuffie fluffed Falkirk’s final chance on 82 minutes.