Airdrie started the game looking the more determined, but it was Falkirk's Andy Thomson who broke the deadlock in the ninth minute when David Nicholls cut the ball into the box for him to net his fourth goal of the season.
Two minutes later referee Kenny Clarke turned down a Falkirk penalty claim when Darryl Duffy was brought down in the box.
The visitors fought back, and Jerome Vareille just missed a chance to convert when keeper Darren Hill missed a cross.
Falkirk struck again in the 25th minute when Nicholls picked up a rebound and blasted a 25-yard volley high into the net.
After the break Falkirk netted number three from a corner by Russell Latapy, which was won by Duffy. The rebound fell to Andrew Lawrie, who forced the ball home from close range.
Eight minutes later Falkirk made it number four when Nicholls spotted Latapy on the far side unmarked, and he beat a defender and hammered home from ten yards.
The rout was completed in the 78th minute when Falkirk's John O'Neil put over a wicked cross and Thomson converted with a diving header for his second of the game.