Stranraer were forced to go again against their Scottish League Two opponents following a 1-1 draw first time around.
After an ordinary first half in their fourth-round replay, the game came to life soon after the interval as Kevin Watt's well-taken finish fired the visitors into a 54th-minute lead.
But Andy Stirling needed just six minutes to pull Stranraer level as he converted from the left side of the penalty area.
Within seconds the hosts had turned the game around as Frank McKeown's right-footed effort found the net from Chris Aitken's corner.
Jamie Longworth and then Martin Grehan added to the scoreline late on to deservedly send the Stranraer through.