The hosts were 2-1 up at the interval and despite some late pressure from the Citizens at Stair Park, Gary Naysmith’s side couldn’t conjure up an equaliser.
However, it’s job done for the Capital men who will now face third-place Elgin City in the first round of the play-offs at Borough Briggs, the first leg taking place on Saturday before the return fixture at Ainslie Park next Tuesday.
Victory for Stranraer also guaranteed them fourth place and they will now face the club that finishes second bottom in League One before the winners meet in the final.
Naysmith made eight changes from the side that defeated Elgin 2-0 on Saturday with striker Blair Henderson earning his first start since dislocating his elbow in the 3-1 win at Cowdenbeath at the end of March.
The home side were fast out of the traps and went ahead just after the 20-minute mark, Andy Stirling firing beyond goalkeeper Ryan Goodfellow from the edge of the area.
The visitors were back level five minutes later in rather fortuitous circumstances. A long Andy Black ball resulted in a breakdown in communication between Scott Robertson and Greg Fleming and the former put the ball into his own net.
Henderson almost turned the game on its head a couple of minutes later when he rattled the crossbar from distance.
Stranraer, however, restored their advantage just before the half-time interval when Thomas Orr outmuscled Conrad Balatoni at the back post to score.
Josh Campbell fired wide ten minutes after the restart before the same player went close with 15 minutes remaining, but Stranraer held on to secure the points they needed.