For Berwick it was another body blow with their failure to make ground on the other relegation candidates plunging them even deeper into trouble.
Rangers made a great start when Darren Smith crashed home a left-foot drive on four minutes.
Stranraer were level almost immediately. Kevin Finlayson crossed from the right, three defenders failed to intercept and Danny Fox netted at the far post.
Fraser Wright headed another Finlayson cross against the crossbar, but Berwick competed well and Kevin Gordon was foiled by a fine double save from Michael McGovern.
Berwick dominated the second half and played surprisingly well in deteriorating conditions, but Stranraer, with their more direct style, showed how to score.
A long ball from the outstanding Wright was picked up by Paul McManus, he outpaced two defenders and calmly swept it past a helpless Gary O'Connor.
Berwick fought to the end and Smith went on a great run past three defenders only to see the ball deflected for a corner.
It was their last chance and now hopes of avoiding relegation are on a knife-edge.