It was a match which opened with plenty of promise. Stranraer pushed for openings and won five corners in the first 12 minutes.
From one of those defender Murray Henderson, who had drifted into the Alloa box, hit a fierce drive which crashed off the underside of the bar and bounced on the line, only to be scrambled clear.
Stranraer kept up the pressure and striker David Graham should have put them ahead when he stole a pass, evaded a tackle and hammered in a tremendous shot from the edge of the box, but keeper James Evans flung himself bravely to his left to touch the ball around the post for yet another corner.
James Stevenson mounted Alloa's first raid, cutting in from the left on a fine run, but finished it with a shot which swung wide.
Richard Walker was gifted a great chance when a Stranraer pass in their own box went astray, but he hurried his shot and drove wildly over.
The turning point came five minutes after the break when Henderson's clearance spun off Christopher Townsley and broke to Stevenson who ran on easily to beat the stranded home keeper Andrew McCondichie and open the scoring.
But from then to the end, it was a tale of missed chance after missed chance for Stranraer, plus more heroics from Evans and at the end, three valuable points for a battling Alloa side.
Brian Crawford, Graham, Lee Sharp, Kevin Gaughan and David Turnbull all had great chances to salvage a point for Stranraer, but it was simply not to be their day.