The home side dominated the game from the kick-off and went in front after 13 minutes. David Hagen sent over a corner from the left and midfielder Graeme Stewart headed in from six yards.
It was 2-0 after 36 minutes when another Hagen corner picked out full-back Craig Tully at the back post and he managed to squeeze a header into the net from the tightest of angles.
The home side had several other chances to extend their lead. Tully hit the post, Stewart fired wide from 25 yards and Robert Linn saw a shot bravely blocked by Shire keeper Tony Mitchell.
Jamie Buchan almost scored soon after the restart when he cleverly weaved his way into space, but his shot was saved by Mitchell.
After 52 minutes Scott Michie shot against the underside of the crossbar only for the ball to bounc clear, but Peterhead extended their lead 11 minutes from the end when Martin Bavidge rose to head in a left wing cross.