Two first-half goals were enough to see Peterhead remain top of the league with their fifth consecutive win.
A stylish performance should have seen them score more goals given the chances they created, but they were never under threat from the moment they took a fourth minute lead.
Jamie Buchan was brought down by a clumsy tackle from defender Gary Kelly and Scott Michie netted from the spot, despite keeper Scott Morrison getting a hand to the ball.
Michie had chances to notch his hat-trick turning and shooting wide from eight yards before forcing a save out of Morrison with a low drive after 19 minutes.
After 24 minutes Peterhead scored a second goal with Michie netting his brace. Martin Bavidge raced through the centre of the East Fife defence before slipping the ball to his left and Michie finished with a well-placed shot low into the far corner.
Michie was very unlucky not to score his hat-trick after 31 minutes when a tremendous shot cracked off the underside of the cross bar and bounced clear.
Man of the match Michie, set up a great chance for Scott Robertson two minutes after the re-start, but the midfielder sent what should have been a tap-in off target.
Keith Gibson went close in the 58th minute hitting the outside of the post after racing past three defenders.
The nearest East Fife came to improving on a record of only two goals in four games came after 70 minutes.
Substitute Brian Fairbairn headed off the post, but that was their only goal threat in the entire 90 minutes.