Stranraer made a great start to the match as David Hamilton fired them ahead with a 22-yard shot that squeezed just inside the upright.
But things went downhill rapidly for the home side after the interval as Paul McManus and Ian Harty teamed up to put the visitors ahead.
Harty set up McManus for the first sending him clear with a well-timed flick on after 55 minutes.
Five minutes later Neil Janczyk intercepted a poor pass back and passed to Harty, who knocked in easily before doubling his tally seven minutes later with a long-range effort.
Brian Fairbairn completed the scoring two minutes from time.