Craig Malcolm was Stranraer's hero as his last-minute strike proved decisive after a spirited challenge from 10-man East Fife.
The striker's left-footed shot from the centre of the box, assisted by Anthony Marenghi, found the top-left corner and settled a tense match.
Both sides had begun the season with victories in the Scottish Challenge Cup against higher-league opposition and the confidence derived from that was reflected on the pitch in an evenly-contested first half.
The tie was in need of a turning point to break the mould, which duly arrived when visiting forward Kevin Smith was dismissed for a crude tackle on Scott Robertson just short of the hour mark.
From there on in the Fifers had their backs firmly to the wall but it was only in the dying seconds that their resistance wilted.