Craig Sibbald's second-half strike was enough for Falkirk to edge past Cowdenbeath and into the fifth round of the Scottish Cup.
Kudus Oyenuga wasted a decent chance for the visitors when he blazed over.
Falkirk's Blair Alston skimmed the crossbar from long-range before Rory Loy forced a good stop from Blue Brazil keeper Robbie Thomson.
Sibbald then put Falkirk ahead on 73 minutes when he reacted quickest to Loy's deflected shot.
Substitute David Smith should have made it two for the Bairns late on but he could only fire over with the goal at his mercy.
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