Managerless Arbroath are still without a point after defeat at Cappielow.
After seven minutes Peter Weatherson drove the ball against the inside of the bar and as it bounced out he was able to knock it back over the line.
Weatherson struck again shortly after the hour mark when he sneaked in at the far post to meet a cross and bundle the ball home.
Arbroath's Greg Henslee scored a header after 78 minutes but the home team could not find another goal.
Morton: Coyle, Collins, Keenan, Greacen, McCulloch, Millar, John Maisano, McAlistair, McClean (Paul Walker 63), Williams (Diack 83), Weatherson. Subs Not Used: Adam, Black, McGurn.
Goals: Weatherson 7 & 65.
Arbroath: Woodcock, McMullen, Rennie, Bishop, Beith (Donaldson 72), McCloud, MacDonald (Cook 82), Henslee, Swankie, Brazil, McLean (Farquharson 68). Subs Not Used: McAulay, Inglis.
Booked: Brazil, Beith, Farquharson. Goals: Henslee 78.
Ref: C Richmond