Goals early in the second half from Steven Thomson and Alan Gow effectively took the game out of the home side's reach and substitute Pedro Moutinho added a third late on.
Roddy McKenzie had to block an early effort from Russell Latapy which he dealt with none too convincingly as Falkirk held the upper-hand.
Gow sent Carl Finnigan clear midway through the first half but McKenzie was alert to the danger and managed to get a hand to the ball.
Gow, in his last game for the club before joining Rangers, was lively enough and tried to catch McKenzie off guard with a curling shot from the corner of the penalty area but it drifted wide of the post.
The excellent Latapy steered a free-kick under the defensive wall seven minutes from the break but McKenzie gathered easily.
Falkirk made the breakthrough three minutes after the break when McKenzie blocked Finnigan but the ball broke to Thomson who squeezed the ball into the net from 15 yards.
Latapy almost scored a second when he side-stepped Greg Shields but his chip landed on the roof of the net.
He played a big part in the second after 57 minutes when he exchanged passes with Gow for the striker to drill the ball home.
Substitute Tom McManus almost pulled a goal back with a late header off the crossbar but by then Falkirk had it wrapped up.
Moutinho added the final goal in the 90th minute with a 20-yard shot which flew past McKenzie.