Peterhead had won their previous two matches and dominated the first 45 minutes but fine goalkeeping plus some bad luck prevented them turning their superiority into a half time lead.
Albion had Myles Hogarth to thank for not being two goals down within the opening ten minutes as the former Hearts keeper made top class saves to deny Stuart McKay and Bobby Linn.
Hogarth then blocked another McKay effort with his legs as the visitors continued to carve out the clearer chances and the crossbar came to Stirling's rescue on the stroke of half time after Linn had sprung the offside trap and chipped the ball over Hogarth's head from long range.
Albion looked totally transformed at the start of the second period and went in front within 60 seconds when Marek Tomana unbalanced the Peterhead defence and Dene Shields found the far corner of the net with a low drive from 12 yards.
Stirling's killer second goal followed 9 minutes later when Paul Hay's free kick was headed home at the back post by Colin Cramb to give the much travelled striker his fifth goal of the season.