Lyle Taylor took his tally for the season to 22 in all competitions with a brace - starting with a close-range finish (19) following good work from Blair Alston.
But Forfar were level two minutes later when Stephen Kingsley impeded Ross Campbell in the area and Iain Campbell powered his penalty into the bottom corner.
The home team restored their advantage on 68 minutes as Stewart Murdoch headed in a corner from Sean Higgins.
Falkirk put the game beyond the visitors when David Weatherston found the bottom corner from 12 yards.
And Taylor added his second seven minutes from time with a close-range volley after Higgins delivered the pass.