A double from Chris Millar – his first goals since returning to Morton from St Johnstone – was enough to clinch victory.
The visitors dominated a low-key first half to turn with a deserved one goal lead when a Michael Tidser free-kick struck the defensive wall and rebounded to Millar. He cleverly beat his man before striking the ball across home keeper Neil Parry and into the net.
In 34 minutes Morton seemed destined to double their lead when top scorer Tidser was put clear by Reghan Tumilty, only for Parry to foil him with a great save.
Opposite keeper Ryan Scully had to match that effort when Alloa’s best chance fell to Jake Hastie, but Scully frustrated him.
Alloa carried their new confidence into dominating the second half but Alan Trouten could only put a clear chance over the bar, then Ton keeper Scully had to hack clear to deal with chaos in his box created by Hastie cutting along the byline, but with eight minutes left Millar rifled a spectacular shot home from 30 metres.