However it was the home side that started the brighter and they almost took the lead within the opening 30 seconds. A poor punch out by keeper Stefan Gonet saw the ball drop to Ritchie Montgomery. He had a free header at goal but nodded wide of the open target.
Morton came close to scoring after 15 minutes when Derek Lilley fired in a dipping drive from 25 yards but it clipped the top of the crossbar with Sean Murdoch beat.
Murdoch pulled off a brilliant stop seconds later with a fingertip push over the bar from a James McAlister drive. But that only delayed the opener. As from the corner Stewart Greacen powered in a header and Lilley turned it home from a yard out.
Morton thought they had doubled their lead four minutes from time when McAlistair's header was nodded home by McGowan but he had strayed into an offside position before getting the vital touch.
McGowan then shot straight at the keeper when he should have scored and McAlistair wasted an even better chance when he was picked out free at the back post but somehow hit his shot against the post.
McGowan gave Morton breathing space in the 61st minute as the visitors doubled their lead. Paul Tosh gave the ball away in midfield and McGowan weaved his way into a shooting position before brilliantly curling a strike beyond the keeper.
Chris Millar looked to have wrapped things up with a well taken goal in the 68th minute from an acute angle on the right but 3 minutes later Barry Donald pulled one back for Forfar with a close range header.
Donald almost made for an interesting finish when he beat the keeper with a 20 yard shot but the ball cracked back off the crossbar.