Declan McManus hit a hat-trick to send the Bairns second.
MATCH REPORT: Peterhead 1 Falkirk 3David Ferguson was sent off after conceding a penalty in the second half.
HOW IT HAPPENED: Matchday LiveMark Durnan's own goal gave the home side a hope in the first half.
Falkirk named former Bairn Graham Bowman as the substitute trialist goalkeeper.