Saints deserved their half-time lead and in fact could have counted more than once but for a sturdy home defence which worked hard to keep the lively visitors out.
It was David van Zanten who was on target for the Paisley side in the 20th minute after a move he started himself on the halfway line. He kept going, swapped passes with Charlie Adam and sent Craig Higgins the wrong way before drilling the ball home.
Stranraer mustered only one real chance before Saints went ahead but when Michael Moore got in his low cross it was perhaps a shade too fast for David Hamilton whose touch sent it sweeping wide.
Saints clearly held the bit between their teeth and did not sit on their lead. They made sure that Barry-John Corr was by far the busier keeper and he made smart saves before the break from Adam and Stewart Kean.
One minute into the second half and visiting keeper Chris Smith saw his first real action with a super save from Hamilton and then again from home skipper Allan Jenkins.
But Smith had no answer as Leigh Hinds equalised after 64 minutes following a great run forward by Jenkins. He calmly picked his spot in the net in a crowded goalmouth to level the scores.
Then just when it seemed that the points would be shared the league leaders grabbed their added time winner in a packed home goalmouth.
Kean came running in at the rear of a long throw in but kept his head and rifled home a superb low strike to win the game for Saints.