Andy McLaren showed the required urgency from the start, forcing Gary McGlynn into a smart, low save from an angular drive. Nevertheless, he showed nerves when he allowed Ross Hamilton to rescue a seemingly-hopeless ball and fire over a dangerous cross which would have been costly if an Alloa striker had been available.
Hamilton himself should have done better with a header after nifty work down the left by Jamie Stevenson, and then Jose Quitongo squandered a wonderful chance when, clean through on David McGurn, he shot tamely at the keeper.
Chris Templeman soared to nod a cross from McLaren past McGlynn, but Michael Bolochoweckyj was perfectly positioned to head off the line. Templeman fluffed another chance after a super Jim McAlistair run, and Ryan Harding caused some anxiety for McGlynn with a mis-hit effort which screwed crazily upwards then dipped suddenly, forcing the Alloa keeper to tip over.
John Ovenstone's on-target header for Alloa was blocked by Hamilton just after the break but, thereafter, it was all Morton. McAlistair scooped over after a wonderful crossfield run and shot by Chris Millar had been parried by McGlynn.
However, the dam broke just after the hour with Paul Walker driving an unstoppable screamer in off the underside of the bar after superb support from McLaren and Millar.
Nine minutes later Millar cracked home a second after a subtle cross from McLaren just a minute after Walker had fired a beauty inches wide from 20 yards.