Morton eventually saw off Montrose with a strong second-half performance.
However, 4-0 was harsh on Montrose, who gave a good account of themselves and could have been in front at the break. The Links Park side won a free-kick 22-yards out in the second minute.
Ross McCord forced a fine save from Nicolas Caraux. Morton responded in the seventh minute with Reece Hands finding Tony Wallace whose low drive was well held.
Morton went close again with Marc Fitzpatrick firing just over from 18 yards after Scott Taggart had got to the byeline.
Morton had a let-off on 20 minutes when Lloyd Young fired against the bar after the Morton defence struggled with a McCord cross. On 25 minutes Wallace forced a fine diving save from Stuart McKenzie.
On the half-hour mark Stephen McNally rescued Stuart Garden’s team when he cleared off the line from a Jonathan Page shot. Dougie Imrie was trying to pull the strings in the middle of the park for the Greenock side.
On 45 minutes Morton boss Allan Moore was shouting at Hands to shoot from a free-kick, but the wall blocked his shot.
After keeping their shape well throughout the first half the Montrose defence would have been frustrated to be carved open just after the break.
Imrie found a great pass sending Modou Cham clear and the striker controlled the ball and volleyed into the bottom right-hand corner.
Montrose went close to an equaliser on the hour mark. Alan Campbell’s header was cleared off the line by Taggart then on the rebound Jonathan Crawford fired over.
Morton hit two goals in stoppage time as Montrose pushed men forward in a bid to rescue the tie. Late finishes by Hands and late sub Aidan Fulton put a slightly unfair reflection on the score.