Livi in a good position
Berwick tried to respond and Willis had a shot from the edge of the box tipped over at full stretch by Gallacher.
But the League 1 side doubled their advantage after 36 minutes when Scott Stewart crossed from the right and Darryl Duffy slid in at the back post to score from a yard out.
The third and match-winning goal came courtesy of sub Leighton Mcintosh after 76 minutes when he prodded the ball home from close range after it fell for him inside the box.
PETERHEAD 0 STIRLING ALBION 2
Peterhead should have taken the lead inside the first minute.
Slackness in the Albion rearguard allowed former player Ross Kavanagh space on the right side of the penalty, but his shot from an angle went a foot beyond the left hand post.
The deadlock was broken in the eighth minute and it was Stirling who notched the opener, Mark Stewart and Peter Mcdonald swopping passes before the latter swept the ball home.
After 16 minutes, Peterhead gave the visitors defence a scare, a Simon Ferry volley 20 yards out taking a deflection off Kyle Banner before flying wide of the right post.
Stirling extended their lead after 72 minutes, the everdangerous Stewart netting following a Jordan Allan corner on the right.
It proved to be too much for Peterhead to pull back.