Kenny McLean almost scored five minutes into his Morton debut. James McAlistair provided him with the pass inside the box, but Tim Woodcock dived low to his left to turn the ball for a corner.
Two minutes later McAllister burst free on the right and his hard, low cross was met by Peter Weatherson who, from four yards, hammered the ball off the bar but, as Jamie Bishop tried to clear, the striker struck out a leg and the ball crashed high into the net.
Midway through the half, Woodcock raced out to intercept a long ball as Weatherson gave chase, but the bounce of the ball deceived him and he had to dive frantically to block Weatherson's attempt to score into the empty net.
A delightful move just before the interval saw McAllister, McLean and Weatherson set up Alex Williams, but the striker dragged the angular drive wide.
Morton attacked relentlessly from the restart and Woodcock saved well from a WIlliams free-kick.
Williams and Chris Miller saw shots whistle just wide before Mark McCulloch's pace took him to the goal line and his cross was just perfect for Weatherson to nod in at the far post from a few yards.
Paul Walker had another shot saved, but Arbroath caused some anxiety among the home support by scoring in a rare raid on the home goal.
Greig Henslee heading in off the underside of the bar following a Gavin Swankie corner.