Tony Wallace and David O'Brien struck in the space of 11 second-half minutes as Morton were too strong for 10-man Albion Rovers in the first round of the Ramsdens Challenge Cup.
Morton took the lead in the 48th minute when Wallace met an inviting O'Brien cross to power a header into the top-left corner.
Wallace had an opportunity to double his tally seven minutes later, but could only shoot wide from close range.
O'Brien got in on the act just before the hour, sweeping home a Michael Tidser's pass.
Rovers' task became even harder 15 minutes from time when Anthony Stevenson received a second yellow card for bringing down Tidser.
Morton could have scored a third, but Jason Naismith headed wide from six yards.
Morton: Gaston, Taggart, Rutkiewicz, Mark McLaughlin (Naismith 71), Dyer, Reid, Wallace (David Graham 77), Stirling, Tidser, O'Brien, Weatherson (Campbell 73). Subs Not Used: Combe, Halsman.
Goals: Wallace 48,O'Brien 59.
Albion Rovers: McCluskey, Reid, O'Byrne, Ciaran Donnelly, Russell, Connor Stevenson, Innes, Anthony Stevenson, Phillips, Dick (Marriott 59), Crooks (Howarth 70). Subs Not Used: McWilliams, Boyle, Brannon.
Sent Off: Anthony Stevenson (75). Booked: Connor Stevenson, Innes.
Ref: John Beaton