Falkirk should have taken the lead with only six minutes gone but Alan Gow's shot after the striker beat the offside trap, trickled inches wide of the upright.
The visitors took the lead in the 27th minute when Kevin James met a Paul Sheerin corner to slam his header into the net with Martin Hardie getting a touch en route.
It was James again who was inexplicably left unmarked at another corner ten minutes later and the skipper took full advantage by directing his header into the net.
Falkirk had not learned their lesson and again allowed James to get his head to a set-piece, glancing the ball into the path of Peter MacDonald to fire into the net with gusto.