Cowdenbeath’s woes in the Championship relegation battle continued as they failed to score for the sixth successive home game.
Cowden opened positively and a long cross from Lewis Toshney was headed on by Colin Nish but Declan Hughes’ finish lacked pace and Jamie MacDonald gathered.
In 19 minutes the home side got in the first meaningful effort when Nish’s nod-on fell for Hughes and his 20-yarder produced a fine save from MacDonald.
Falkirk went down the left in 25 minutes and a fine cross by Luke Leahy looked good for Botti Biabi but the striker mistimed his run and the ball rolled out.
At the other end, Bairns defender Will Vaulks got in a fankle, with Nish and Hughes threatening from Sean Higgins’ lay-off, and, in attempting to clear, the defender hit his own post.
In 52 minutes, the breakthrough came for the Bairns. Tom Taiwo got space on the right and his cross was perfect for John Baird to head past Robbie Thomson.
As Falkirk stepped up their game, Biabi got away from John Armstrong but his low 17-yarder was held by Thomson.
With 13 minutes to go, Falkirk threatened again when sub Alex Cooper sent over a lovely cross from the left but Thomson dived to smother the ball.
With seven minutes left, Cowden’s Kenny Adamson was red carded for a wild tackle on Baird.