Ryan Strachan fired the home side into a 59th minute lead and the league's top scorer Rory McAllister soon added a second.
A 77th minute own goal by Ricky McIntosh of Montrose put Peterhead out of sight and McAllister doubled his personal tally with a slick finish four minutes from time.
Annan Athletic remain eight points behind Peterhead after an excellent 3-0 victory at third-placed Clyde.
Scott Davidson struck a 41st minute opener for Annan, who saw off their Cumbernauld hosts easily thanks to a second-half double from Josh Todd.
Stirling Albion came from behind to beat Berwick Rangers 2-1 at Forthbank. Darren Lavery struck a fine opener for Berwick in the 39th minute, but the visitors' Paul Currie was sent off for an unruly gesture.
David Weatherston levelled in the 89th minute before Sandy Cunningham completed a dramatic comeback with an excellent header in stoppage time.
Albion Rovers still have an outside chance of reaching the play-offs as they climbed to sixth with a 2-1 victory over off-colour East Stirling.
Ryan Donnelly's double proved enough for Rovers, although Scott Maxwell did notch an 81st minute consolation for Shire.
Bottom club Queen's Park registered a 1-1 draw at second bottom Elgin City. Eamonn Brophy had given Queen's Park a third minute breakthrough only for Elgin's Dennis Wyness to equalise shortly after half-time.