The early stages of the first half were slowly but surely dominated by the visitors, and home keeper Barry-John Corr had to look lively to field drives from Mark McCulloch, twice, and Alex Burke before County finally hit the score sheet after 34 minutes.
Neil McDonald set up the opener, but his pass was well anticipated by Don Cowie who had drifted away from his marker and had only to turn and shoot past Corr at close range.
Stranraer had been struggling, and their prospects looked bleak after that opening score until Michael Moore took a hand in the 44th minute. His clever pass caught County's defence flat-footed and David Hamilton latched on to it and netted with a looping shot.
Hardly had the cheering died when Stranraer struck again. Lee Sharp put a cross into the box which McDonald blatantly handled, and from the resultant penalty kick Hamilton grabbed his second goal within a minute to send Stranraer in at the break a goal ahead.
Measured by pleasure it was a daft half-time score, but County took only nine minutes to claw their way back into the game, drawing level when Alex Burke delivered a low cross and Cowie pounced to get his second goal of the day in an unguarded goal mouth.
Eight minutes from time, during a spell in which Stranraer had looked as good as their visitors, it was Ross County who snatched the winner. Again John Rankin was totally unmarked as he took a deep cross from the right just outside the six-yard box. His first drive struck defender Derek Wingate but Rankin kept his cool, collected the loose rebound and hammered home a golden goal for County.