In the opening minutes Morton showed that they were in the mood to continue their winning ways, with a close-range shot from Derek Lilley in five minutes and a fierce 20-yard in eight minutes later touched over the bar by Allan Creer.
Steven McKeown came to Alloa's rescue in 19 minutes when with the keeper beaten he cleared a Derek Lilley shot from the line.
Against the opening run of play it was Alloa who snatched the lead in the 22nd minute when Graeme Brown hooked an overhead shot from a Jon Ovenstone corner, beating Morton keeper David McGurn low to his right.
In the 25th minute Morton came close when a mix-up with the Alloa defence allowed Paul McGowan to have a free shot on goal, but his weak attempt went wide and came to nothing.
Alloa dramatically extended their lead in the 22nd minute when Ross Clarke from 20 yards out hit an unstoppable free-kick which beat the Morton defence and McGurn in the Morton goal.
Eight minutes later Morton pulled one back when Peter Weatherson fired home a 25-yard free-kick, this goal gave Morton a lift and their play became more intense.
Yet it was Alloa who scored in the 40th minute when Graeme Brown extended the lead when from close range he deflected a Clarke shot into the net.
In the 65th minute Weatherson was on hand to head home a perfectly placed Jamie Stevenson corner kick to make the score 3-2.
Morton threw everything they had at the Alloa defence to try and break through for an equaliser, but outstanding defending from Stuart Malcolm and substitute Robert Sloan kept the attacks at bay and in the closing minutes thwarted several attempts on the equaliser.
In the closing minute a Paul McGowan shot came through a packed Alloa defence and somehow Creer managed to stop the ball from going in.