A Tony Andreu header midway through the second half was all that separated the sides as Stranraer emerged with huge credit against their more illustrious opponents.
Indeed, had a late Christian Nade effort been a couple of inches lower, the League One outfit would have forced extra time at the least.
Instead United held firm and, while their priority may be an immediate return to the Premiership, Ray McKinnon’s side can perhaps look forward to an extended run in this competition though they will surely have to improve on this showing.
A lively opening saw both sides commit to attack though poor finishing proved a common denominator.
However, the deadlock was almost broken when Andreu sent a 20-yard free kick crashing off a post with Cammy Belford in the home goal struggling. Belford then watched as Simon Murray’s header slipped inches wide.
There was action for United keeper Luis Zwick who did brilliantly to parry Willie Gibson’s fierce angled drive.
That effort was matched at the other end when Belford produced a crucial save to deny the lively Murray. Stranraer might have found an opener when Craig Malcolm ran through but was flagged offside.
But the decisive moment went in United’s favour when Andreu found space to get on the end of a Paul Dixon cross and place his header beyond the despairing Belford.
The Tangerines survived a few anxious moment late on – none more so than when substitute Nade volleyed inches over in stoppage time.