The visitors enjoyed the bulk of the play throughout but it was Stranraer, fighting to preserve there first division status, who hit a 19th-minute opener against the run of play.
Lee Sharp swung a corner over which was headed goalwards by David Hamilton. His effort was swept from the visitors' goal-line but Stephen Swift stepped onto the clearance and hammered a shot home from 12 yards.
The Jags pressed forward in search of an equaliser but they found home keeper Barry-John Corr in top form, as the former Motherwell man blocked shots from Billy Gibson and Darren Brady.
After the interval Thistle took total command and Stranraer had a let off when Scott McCulloch thundered a 30-yard angled free-kick inches wide off Corr's near post.
A minute later he tried the same trick again from the same spot after a foul by Derek Wingate. This time McCulloch's fierce drive hurtled past Corr for the leveller. Wingate tried to block his shot but its pace was too much for the defender.
Seven minutes later the Jags inched ahead when Mark Roberts rose above the stationary home defence and headed Adam Strachan's cross beyond Corr.
With a quarter of an hour remaining, Thistle all but clinched the tie from the penalty spot. Wingate was adjudged to have fouled Billy Gibson and Roberts struck for the second time, sending a rising spot-kick wide of the diving keeper.
Stranraer's tempers frayed and both Alex Keddie and Bryan Gilfillan saw red in injury-time after a melee.