The home side were first to threaten when Sean Kilgannon was released on the left by Kevin Fotheringham in the second minute, but the Rovers midfielder lobbed narrowly over after spotting Cowden keeper David Orr off his line.
Mixu Paatelainen's men gradually assumed control after this early escape and they forged ahead after 11 minutes when a corner on the left from Morgaro Gomis was met by former Rovers man Pat Clarke, who sent a powerful header beyond the reach of Michael Brown.
Clarke found himself in front of Brown a few minutes later, but the Beath striker was denied by a last-ditch tachle from Steve Bonar.
The visitors almost increased their lead after 23 minutes when another former Raith player, Laurie Ellis, saw his header rebound from the crossbar.
Both Armand One and Sean Kilgannon tested Orr in the latter stages of the first half, but the keeper ensured his team retained their advantage at the interval.
Raith were fortunate not to go further behind after 58 minutes when Iain Davidson sliced a clearance against his own crossbar.
The Kirkcaldy men equalised after 72 minutes, however, when substitute Stephen Manson fired home after Orr had fumbled a cross from Chris Silvestro.
A draw appeared to be the likely outcome, but two late strikes from Markus Paatelainen and Clarke ensured victory for Cowden.