It did not take long for Morton to assume control. Jamie Stevenson's cross was heading for the head of Derek Lilley, but Stuart Malcolm made a vital intervention to prevent an early score.
The Ton went ahead on 12 minutes. Alloa failed to clear a Jim McAlistair throw-in, allowing Lilley to feed Paul McGowan, who swept a low, angled shot past Allan Creer from ten yards.
Creer made an acrobatic save from Weatherson's free-kick then saved a long-range drive from Scott McLaughlin, before Ryan Harding had a shot deflected wide.
Stewart Greacen sent a header wide before Ton scored a marvellous second. McGowan cleverly won the ball in the centre circle and waltzed his way past four or five opponents before threading the ball through for Lilley, who had timed his run perfectly, to stroke it past Creer from ten yards.
In a rare Alloa raid, Graeme Brown volleyed over an excellent Kieran McAnespie cross, but Stevenson ended the first half with a powerful free-kick which cannoned off Creer's chest.
Another Greacen header just cleared the bar and Creer saved from McAlistair before Chris Millar scored a sublime third.
Stevenson showed admirable control to feed McGowan who, in turn, lofted the ball over the defence for Millar to turn the ball past Creer.
McAnespie forced David McGurn into a save from a rising drive, but sub Chris Templeman sealed a marvellous performance for the league leaders when he connected with Stevenson's cross to send a looping header over the overworked Creer.