Morton turned in an impressive display as they took another major step towards the Second Division title.
The table toppers took the lead after nine minutes when Jamie Stevenson scored from the penalty spot.
Morton doubled their lead after 28 minutes when Paul McGowan reacted first to knock home a rebound from one yard.
Morton secured the points with a third after 70 minutes when McGowan followed up to net after Stevenson's initial shot was blocked by keeper David Hay.
Morton: Mathers, Weatherson, Macgregor, Harding, Greacen (Walker 73), McLaughlin, Finlayson, Stevenson, Templeman, McGowan (Linn 80), McAlistair. Subs Not Used: Millar, Russell, McGurn.
Goals: Stevenson 9 pen, McGowan 28, 70.
Cowdenbeath: Hay, Baxter, Ellis, Armstrong (Dalziel 61), Hill, Kenneth, Clarke, Lennon (McBride 75), Buchanan, Patrick Scullion, Fotheringham. Subs Not Used: Weir, Bryan, Allison.
Booked: Armstrong, Fotheringham, Clarke.
Ref: S Nicholls