Stranraer got away to a great start on their second division return, wearing down a stuffy Alloa side and then emphasising their superiority with three well-taken goals.
The first period produced a blank score sheet, but David Graham could have given The Blues a second minute lead, but for a super save from Gary McGlynn.
The Alloa keeper went on to make another two good stops from Graham and then, with the best save of the half, denied Stranraer new boy John Fraser, when he unleashed a powerful low drive from 30 yards.
The talking point of the first half, however, was referee Brian Cassidy turning down a solid penalty claim right on the interval, when Alloa's Paul Mortimer clearly downed Graham in the box.
The visitors had plugged away bravely to keep Stranraer out, but after the break the roof fell in on them.
The first crack appeared in 56 minutes when Graham stole the ball from Alloa skipper Brown Ferguson ran almost half the length of the field and rounded McGlynn before hitting the net.
Then on 79 minutes it was Graham again, picking up a header from Kevin Gaughan and repeating his run around the keeper before touching home a second goal.
Four minutes from time Graham turned goal maker, laying on a cross for Stephen Swift to head home and round off an emphatic victory.