Loan star Declan McManus netted the first goal of his second spell with the club, and his 13th of the campaign, when he opened the scoring right on the stroke of half-time.
Ross Caldwell seized on a moment of hesitancy in the visitors’ ranks to get on the end of Conor Pepper’s prodded pass and tee up strike-partner McManus for a tap in.
Stevie Aitken’s table toppers pushed for an equaliser in the second half but found Jim Duffy’s defence a tough nut to crack, with Ricki Lamie and Sean Crighton both rocks at the back.
And the Ton wrapped up a vital victory in injury time when teenager Mark Russell collected a Joe McKee pass and waltzed past two challenges before coolly firing under David Mitchell.
Elsewhere, third-placed Forfar Athletic beat Dunfermline 1-0 at Station Park to stay level on points with the Ton and leave things incredibly tight at the top of League One.
Morton (4-4-2): Gaston ©; Kilday, Crighton, Lamie, Russell; Pepper, O’Ware, Forbes (McKee, 82), J. McCluskey (S. McCluskey, 69); McManus, Caldwell.
Subs not used: Tennent, Milojevic, Scullion, Caraux (gk).
Stranraer (4-4-2): Mitchell; Pettigrew, Robertson, McKeown ©, Longridge; Gallagher, Bell, C. Aitken, Gibson (Stirling, 79); McShane (Malcolm, 63), Longworth Subs not used: Winter, Russell, Tobin (gk).
Booked: Longridge (29).
Attendance: 1,921 Referee: John McKendrick
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