It was Montrose who went close to scoring after five minutes when Martin Wood collected a loose ball and fired a shot against the post.
A minute later a Kevin Webster free-kick was saved by Paul Mathers.
In the eighth minute David Hagen broke on the left and shot just wide of the post.
In the tenth minute a shot from Wood was saved by Mathers and Stephen Fraser shot wide from the rebound.
In the 17th minute a Keith Gibson header came back of the Montrose crossbar.
Montrose pressed in the closing minutes of the first half and Paul Doyle drove a free-kick just wide and then Wood had a shot saved by Mathers.
Peterhead open the scoring in the 55th minute. A Gibson header was parried by James Butter and Scott Michie shot into the empty net.
Montrose tried to reply and Graeme Sharp shot just wide of the post.
Fraser burst into the box in the 71st minute and was denied by Mathers and five minutes later Wood collected a Calum Watson pass and again forced a save from the goalkeeper.
Peterhead wrapped things up in the 79th minute when Martin Bavidge was tripped and Michie scored from the spot.