Aberdeen scored twice in extra-time to overcome Morton and book a place in the last 16 of the Scottish Communities League Cup.
Gavin Rae had the first half's best chance but could not beat Derek Gaston.
Gaston continued to keep the Dons at bay in the second half and Morton's Archie Campbell had an effort saved by Jamie Langfield.
With penalties looming, Rae headed home in the 109th minute and then set up Scott Vernon for a late second.
The remaining second-round ties take place next midweek, after which Aberdeen will learn their third-round opponents.
And the Dons will be pleased to be in the draw after avoiding the kind of defeat to lower league opposition which has dogged them in recent seasons.
Langfield leapt to his right to keep out Stephen Stirling's long-range shot as Morton asserted themselves early on.
The visitors responded with Ryan Jack's drive stinging the palms of Gaston.
And the Dons should have moved ahead after Ryan Fraser's cross was cleared as far as Rae, who could not beat Gaston from a promising position.
Peter Weatherson was off target with a couple of efforts for Morton before Aberdeen were forced into a change with Chris Clark replacing Stephen Hughes.
Morton made life difficult for Aberdeen at Cappielow
The stalemate continued at the start of the second half with Aberdeen's Jonny Hayes and Morton's David O'Brien firing wide.
The visitors began to create the better chances and Rae was close with a shot from the edge of the box before Scott Vernon headed past the post.
Gaston denied Rae twice in the space of a few minutes as Morton continued to be pinned back.
However, Morton almost took the lead against the run of play when Fouad Bachirou released Weatherson's replacement Archie Campbell through on goal and the forward's shot was touched onto the bar by Langfield.
Campbell caused Aberdeen further problems in the closing stages of regulation time but Morton could not convert several openings.
This pattern was repeated in the opening period of extra-time with David Graham's teasing ball across the six-yard line finding no takers.
Morton got plenty of bodies back every time Aberdeen came forward and penalties became an ever more likely outcome.
But Rae finally broke the deadlock when he met Hayes' cross and nodded home his first Aberdeen goal.
And Rae then turned provider as he unselfishly played in Vernon on the break, giving the striker his maiden goal for the season.
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