Morton booked a Scottish Cup fifth-round tie away to Dundee after Peter Weatherson's hat-trick helped them thrash Turriff United.
Having drawn 1-1 at The Haughs, the Highlanders hoped to pull off a shock in the replay in Greenock.
But Weatherson's 37th-minute strike followed by Michael Tidser's penalty made it 2-0 at the break.
Tidser struck his second, then Peter MacDonald headed The Ton's fourth before Weatherson added two more.
The hosts' early forays saw Weatherson twice came close with his head inside 16 minutes.
Team-mate Archibald Campbell fired over the bar soon after, while David O'Brien forced a save out of visiting goalkeeper Stephen Coutts.
Weatherson, who scored Morton's goal in the first match between the sides, opened the scoring when he rifled in a shot from the edge of the box to give the home side a deserved lead.
Turriff's woes deepened a minute before the interval as defender Ross Anderson fouled Michael Tidser inside the box, and the midfielder, who scored twice in Morton's 3-0 replay win over Albion, had no problems dispatching the penalty.
Weatherson turned provider for Tidser's second goal on 63 minutes, the latter drilling past Coutts from 25 yards.
MacDonald then extended the home side's advantage with a headed goal from point-blank range.
Weatherson's second and third of the evening swiftly followed, both goals coming within three minutes of each other.
His second strike was a cool close-range finish while he completed his treble by rifling home from 12 yards.
Morton: Gaston, Taggart, Reid, Mark McLaughlin, Dyer, Graham (Wallace 69), Bachirou (Wilkie 74), Tidser, O'Brien, Weatherson, Campbell (MacDonald 60). Subs Not Used: Hutton, O'Ware.
Booked: Mark McLaughlin.
Goals: Weatherson 37, Tidser 45 pen, 63, MacDonald 77, Weatherson 82, 84.
Turriff United: Coutts, Gary Davidson (James Chalmers 64), Anderson, Simpson, Herd, Young, Lewis Davidson, Ligertwood (Fraser 75), Gray, Harris (Gauld 46), Robbie Henderson. Subs Not Used: Gatt, Campbell.
Ref: Gary Hilland