In cold storage for two weeks due to the weather, the visitors exploded out of the blocks and would have been ahead after 60 seconds but Ryan McCallum missed a free header.
A terrible back-pass then gave Cowdenbeath's Iain Mauchlen a sight of goal, but keeper John Dodds blocked with his legs.
East Fife's John Martin was denied after 11 minutes when David Hay tipped his header over the bar.
Cowdenbeath didn't learn the lesson, and Sean Paliczka stole in at the front post on 13 minutes to head in a corner.
Gary Kelly then cut inside after 18 minutes and drove a low shot into the bottom corner. Gavin Beith had a chance to finish Blue Brazil after 40 minutes, but he screwed his shot wide while Mikko Paatelainen was foiled at the other end by John Dodds' sound goalkeeping.
Cowden's Markus Paatelainen almost hit back straight from the whistle, but Dodds again saved.
John Ward gave the visitors hope in the 55th minute when he fired a loose ball through a ruck of players and into the net.
McCallum had a header deflected over the bar as Cowden threatened to level, and Dougie Hill just missed the top corner with a strike after77 minutes.
With just four minutes left Mikko Paatelainen almost grabbed a leveler, but Dodds somehow clawed his shot around the post.