Lyle Taylor took his tally for the season to 22 in all competitions with a brace. He put the First Division outfit ahead in the 19th minute with a close-range finish following good work from Blair Alston.
But Forfar were level two minutes later. Stephen Kingsley impeded Ross Campbell in the area and Iain Campbell powered his penalty into the bottom corner.
Falkirk re-took the lead in the 68th minute as Stewart Murdoch headed in Sean Higgins' corner.
Seven minutes later David Weatherston gave his side a two-goal cushion with a low shot into the bottom corner from 12 yards.
Taylor added his second seven minutes from time with a close-range volley from Higgins' cross.