Division Two leaders Morton secured three points in a hard-fought win in treacherous conditions at Cappielow.
Alloa struck the opener after 10 minutes when Chris Mackie pounced to fire home after Ross Clark's free-kick was not cleared.
Chris Templeman fashioned an equaliser after 65 minutes when he lost his marker on the edge of the area and drilled a shot into the net.
Peter Weatherson's scored the winner 14 minutes later with a 20-yard strike.
Morton: Mathers, Macgregor, Harding, Greacen, Weatherson, Millar, Stevenson (Finlayson 56), Keenan (Linn 56), McAlistair,Templeman, McGowen. Subs Not Used: Walker, Lilley, McGurn.
Goals: Templeman 65, Weatherson 79.
Alloa: Creer, Forest, Malcolm, McColligan (Stuart 86), McKeown, Bolochoweckjy (Sloan 83), Clark, Grant, McAnespie, Mackie, McClune. Subs Not Used: Comrie, Kelly, Hutton.
Goals: Mackie 10.
Ref: D Sommers