Cowdenbeath attacked from the start and Gary Fusco missed a free header from Martin Fotheringham's corner, but moments later Liam Buchanan crossed from the right and Pat Clarke scored with a simple tap-in.
Buchanan then had a goal disallowed for offside while Markus Paatelainen and Fusco both went close to maintain the pressure on the visitors.
Morgaro Gomis eventually made it 2-0 with his first goal for the club, the French midfielder firing a left-foot drive into the top corner from 20 yards.
Peterhead had to get one back quickly and Chris Hegarty did the job with a stunning low free-kick from long range.
The visitors pulled level shortly before half-time when home skipper Innes Ritchie tripped Graeme Sharp and Bobby Linn slotted home the penalty.
Cowdenbeath came out flying after the break and veteran keeper Paul Mathers made an amazing reflex stop to block Ritchie's header.
Paatelainen wasted a glaring chance and Fotheringham clipped the top of the bar from distance and it was from yet another Fotheringham free-kick that Cowdenbeath edged ahead again, as Buchanan bundled the ball home inside a crowded penalty area.
Substitute Scott Dalziel finally killed Peterhead off with a measured finish with the outside of his right foot seven minutes from time.