Peterhead could have taken the lead inside the opening minute when Jordan Brown attempted a long-range effort from 35 yards out, but it did not get the better of the keeper.
However, Stranraer took the lead against the run of play with just under 20 minutes gone, as William Gibson picked out the top left corner directly from a free kick.
The visitors tried to get back on level terms just before the break when Jamie Redman tried to head in from close range, but he could not get the better of Mitchell.
Peterhead struggled to cope with Stranraer's pace and dominant possession late on, letting another in when Sean Winter crossed the ball in for Longworth to add his second of the night.
The hosts made it five just before full time when Daniel Storey carved out some space in the box before rifling the ball into the bottom corner to complete an emphatic win.
Stranraer now sit five points behind leaders Forfar Athletic, while Peterhead are seventh in the table.