A goal seven minutes ahead of half-time from striker Scott Michie was enough to give Peterhead three important points.
The visitors dominated throughout and only a fine display from home keeper Michael Hankinson prevented them from winning by a far greater margin.
Hankinson was first in action after ten minutes when he kept out a header from Martin Bavidge.
Seven minutes later Bavidge found himself in on goal but the keeper made a good block at the expense of a corner.
In 32 minutes a good turn by Bavidge lost his marker but again Hankinson managed to save.
The breakthrough came in 37 minutes when Michie netted with a powerful shot from a Bavidge cut back.
Peterhead looked to add to their tally and four minutes from half-time Michie found himself through on goal but Michael Hankinson managed to save with his legs.
Montrose were an improved side in the second half and after 61 minutes Graeme Sharp was denied by a good stop from Paul Mathers.
Back came Peterhead and when Michie put Bavidge through, Hankinson made a good save at the edge of his box.
Montrose refused to give up and an effort from Euen Hall just cleared the bar.
Home hero Hankinson made another good save from Keith Gibson in the 79th minute and then seven minutes from time he again saved well from Michie.
Montrose almost snatched an equaliser in the 87th minute when a Steven Kerrigan header was kept out by Mathers.