While Motherwell’s progression to the quarter-finals was a straightforward one, fellow SPL sides St Mirren and Aberdeen will have to negotiate replays if they are to book a place in the last eight.
The home side stunned their Irn Bru First Division opponents as they raced into a 5-0 half-time advantage.
Motherwell announced their intentions with four minutes on the clock as Morton keeper Colin Stewart struggled to deal with a back pass. The ball broke to Jamie Murphy, who hit the side netting.
However, Tom Hateley scored directly from a corner before Murphy, Shaun Hutchinson, newly-arrived Estonian striker Henrik Ojamaa and Nicky Law all netted for the hosts as the tie was all but decided before the interval.
Murphy then blasted home his second goal midway through the second half to complete a one-sided scoreline.
It took Morton nearly an hour to muster an attempt on goal.
On 56 minutes, Peter MacDonald did well to get his shot away, but keeper Darren Randolph gathered easily.
McCall said: “Hopefully, having to play one game less than our opponents will give us a little edge over them when we meet in the league.
“It was a professional job. We asked at the beginning of the game for a high tempo as we couldn’t afford to go out and take liberties or we would be in for a rude awakening.”
He added: “I am delighted that we have been able to address our poor home form in recent weeks.
“We had a team meeting and discussed three massive home fixtures. It is very pleasing that we have managed to win all three and score 12 goals in the process.”
McCall was delighted to see the goals shared around the team as Motherwell pushed up their tally with only three in reply over those three matches.
“I have been looking for Nicky [Law] to add goals to his game and he has now scored two in our last three games. It was also good to see Shaun Hutchinson score, he regularly goes up for corners, and we spoke to him about getting on the end of them more regularly.”
Morton manager Allan Moore said his side must pick themselves up after slumping to a heavy defeat.
The First Division side were unable to cope with Motherwell’s attacking threat in the first-half at Fir Park.
“I thought this could have been a real morale problem for our league campaign.
“We took a big support with us to Motherwell and certain individuals let us and them down,” said Moore.
“We must pick ourselves up quickly from what was a painful day for everyone.”