The Bairns made three changes to the side that drew with Cove as Leon McCann, Aidan Keena and Steven Hetherington came in for Cammy Williamson, Jaime Wilson and Seb Ross who all dropped to the bench.
Hetherington was also wearing the captain’s armband with head coach Paul Sheerin confirming after the game that the Englishman had replaced Gary Miller as club captain.
The former Alloa midfielder’s first action in that role was to bring down Andre McCarthy in the penalty area after just two minutes for what looked like a stonewall penalty but referee Matthew MacDermind wasn’t interested as the visiting players swarmed him in protestation.
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The early stages were evenly poised and end to end as Callumn Morrison, once again the obvious focus point for the hosts, cutting in from the right and forcing Brett Long in to a good save.
Peterhead responded with Jamie Ritchie hitting a low effort through a crowded penalty area which had Robbie Mutch beaten but came back off the post.
However, Falkirk responded to that scare and had netted the opening goal on 36 minutes when Morrison’s cross from the right was perfectly judged for Craig McGuffie to rise highest at six yards and head in his first ever goal for the Bairns.
The hosts started the second half the brighter and were 2-0 up ten minutes after the break as Morrison's corner dropped to Nesbitt whose shot was blocked but fell to Paul Dixon who manged to turn inside the area and curl a terrific effort around Long and in off the underside of the bar.
Morrison had a great chance to make it 3-0 on 76 minutes when he cut in from the right again and had yards of space on the edge of the area but shot straight at Long.
The icing nearly went on the cake in the closing stages as Ompreon, on midway through the half for Keena, nearly bagged a debut goal after great play by Morrison and Charlie Telfer but Long was able block his effort.
With the last kick of the ball the visitors bagged a consolation goal as substitute Jordon Brown stabbed a close range effort past Mutch three minutes in to injury time but it was too little too late.