Clyde, who are currently top League Two, went ahead after 14 minutes, Kieran MacDonald placing a header straight into the top-left corner of the net after a great cross by Stuart McColm.
But Longworth's strike put paid to any hopes of an upset. The former Queen's Park man has scored nine times in the league since signing for Stranraer in the summer, and added a cup goal to his tally by converting from close range.
Stranraer could have won it but strikes from Martin Grehan and Scott Robertson narrowly missed the target meaning a replay will be required to decide the tie.
- Sports & Recreation