The visitors dominated the first half with lively young striker Liam Buchanan their main threat. He could have scored in the 21st minute after running clear, but home keeper Paul Mathers tipped the ball over for a corner.
Two minutes later Buchanan set up Scott Dalziel who saw his shot blocked by Mathers. Ten minutes later Buchanan sent a volley into the arms of Mathers from the edge of the penalty area.
Peterhead scored what proved to be the winner ten minutes from half-time. Martin Bavidge burst into the right side of the penalty area, he cut the ball back from the byline and defender Graham Guy turned the ball into his own net from a couple of yards out.
The second half belonged to Peterhead and they should have built on their lead. Graeme Sharp raced clear, but had his shot blocked by keeper David Hay, who then saved twice in a minute from Martin Wood before defender Mark Perry sent a shot off the crossbar.
Bavidge then Gibson went close with long-range efforts, before Cowdenbeath almost snatched a point with a late chance from substitute Mark Baxter, but his shot through a ruck of players went wide.