A win for the visitors would have taken them above Ayr United into second but Joe Cardle's strike condemned them to a sixth straight loss.
Cardle netted the winner when he converted from Ryan Wallace's pass.
The Pars go up to the Championship having finished 18 points clear, while Peterhead will take on Ayr in the promotion play-off semi-final.
Champions Dunfermline Athletic beat Peterhead before being presented with the Scottish League One trophy.