Falkirk dominated possession in the opening stages andAlex Jakubiak stabbed home from close range to open the scoring after a well-worked move.
Connor Hazard made two excellent saves to deny Gallagher and Danny Handling, but the same pair combined when Handling set up Gallagher to level from 12 yards.
Falkirk, though, stepped up several gears to take control on the restart when first Longridge produced a fine solo effort to re-establish the lead.
Tommy Robson then produced a brilliant finish off an upright before Craig Sibbald steadied himself on the edge of the box and drilled home.
Joe McKee hit a fifth for the visitors before Liam Burt’s consolation for Sons.