Morton fended off a comeback from Cowdenbeath in the second round of the Challenge Cup.
The home side eased into a three-goal lead with Scott McLaughlin's fierce 20-yard shot opening their account.
Paul McGowan unleashed an unstoppable shot from 18 yards and Chris Millar's drilled strike extended Morton's lead.
Pat Clarke swept the ball in from eight yards and Martin Fotheringham scored with an 18-yard free-kick for the visitors but Morton held on.
Morton: McGurn, Finlayson, Harding, Weatherson, Walker (Keenan 41), Millar, Jamie Stevenson, McLaughlin, McAlistair, Lilley, McGowen (Templeman 46).
Subs Not Used: McClean, Russell, Gonnet. Booked: McGurn.
Goals: McLaughlin 10, McGowen 12, Millar 16.
Cowdenbeath: Orr, Guy (Buchanan 86), Patrick Scullion (Fusco 80), Hughes, Kevin McBride, Baxter, Gomis, Clarke, Ellis (Ritchie 64), Fotheringham, Paatelainen.
Subs Not Used: Paul McBride, Allison.
Booked: Kevin McBride, Patrick Scullion, Fusco.
Goals: Clarke 48, Fotheringham 61.
Ref: W Bollum (Scotland).