A controversial game saw Stranraer midfielder Rober Walker sent off and assistant manager Derek Ferguson sent to the stand for a remark to the referee.
A poor first half was brought to life with a stunning strike from Linn in the 29th minute. His shot from 25 yards flew into the top left-hand corner of the net.
He scored again two minutes before half-time, latching on to a long kick-out from keeper Paul Mathers to score with a low shot from just inside the penalty area.
Stranraer were back in the game 10 minutes after the re-start. Captain Michael Moore played the ball to David Hamilton, and he lobbed Paul Mathers to get his side back into the game.
Three minutes later Moore hit the post, but any chance of a comeback was ended when Linn scored his hat-trick soon after bursting through the heart of the visitors' defence to score from 12 yards.
Walker was booked twice in the space of two minutes mid way through the second half to leave his side down to 10 men. Bryan Gilfillan then punished Stranraer with a fourth, diving to head in from close range.
Alex Burns coolly shot home a second goal for the visitors, but Linn netted his fourth from a tight angle to wrap up the points 10 minutes from the end.