Andy Rodgers netted the opener after only three minutes and with four minutes remaining, Peterhead made certain of the three points as Fraser McLaren scored.
Annan Athletic stay second despite suffering a 3-2 loss at the hands of East Stirling at Galabank.
Maxwell Wright fired Shire ahead in the 21st minute but, after Scott Davidson equalised from the penalty spot, Andrew Mitchell's 48th minute strike swung the match in Annan's favour.
However, East Stirling drew level through David Greenhill before Nathan Shepherd struck an 87th minute winner.
Barry Wilson recorded his first victory as Elgin City manager as his side earned a 3-2 win at Berwick Rangers, who lost for the first time under player-manager Colin Cameron.
Stirling Albion climbed to fifth in the table after a well-earned 2-0 victory over Albion Rovers at Forthbank.
And Queen's Park are now 13 points adrift at the bottom of the league after slipping to a 1-0 defeat at Montrose.