The game was settled in the early stages of the second half when Craig Malcolm and Andy Stirling netted within two minutes of each other.
Malcolm broke the deadlock after 52 minutes with a low effort from close range before Stirling's left-footed strike doubled Stranraer's lead.
Scott McBride wasted Albion's best chance as Stranraer claimed the points.
Stranraer scored two quick-fire goals to see off Albion and record their third successive win.