Daniel Moore scored a penalty double for the hosts in the second half. Peterhead finished the match with eight men after Callum MacDonald, Steven Noble and Stuart Ross were all sent off.
Queen's Park moved into third place after a hard-fought 1-0 success against Clyde at Hampden. Ian Watt scored the only goal in the 27th minute.
Montrose ran out comfortable 3-1 winners over Berwick Rangers at Links Park. Leighton McIntosh volleyed the hosts ahead after 29 minutes and David Grey added a second from the spot.
Darren Lavery pulled one back on the stroke of half-time but McIntosh added his second in the 77th minute.
East Stirling earned their first points of the campaign by beating Stirling Albion 3-1 at Ochilview. Albion's Scott Davidson was sent off for violent conduct in the 27th minute but his team opened the scoring through Mark Ferry early in the second half.
But Scott Maxwell levelled and David Greenhill and Nathan Shepherd netted in the last 10 minutes to give East Stirling the win.