The draw sends 'Ton back to Cliftonhill, which was the scene of a tough tie for the club in 2012. The Greenock men needed a replay to see Rovers off after struggling to a 1-1 draw in Coatbridge.
Rovers are currently riding high in League One, sitting in third place in the table.
The tie, to be played on Saturday 28 November, also takes 'Ton keeper Derek Gaston back to his old club.
Full draw: Stranraer v Buckie Thistle Queen's Park v Forfar Athletic Formatine United v Fort William/Cove Rangers Dumbarton v Alloa Athletic East Fife/Stirling Albion v Cumbernauld Colts Albion Rovers v Greenock Morton Falkirk v Turriff United/Fraserburgh Nairn County/Wick Academy v Linlithgow Rose Peterhead v Livingston Huntly v Lothian Thistle /Montrose Elgin City v Raith Rovers Airdrieonians v Brechin City Ayr United v Dunfermline Athletic Inverurie Loco Works v Annan Athletic Stenhousemuir v East Kilbride/Forres Mechanics Cowdenbeath v Arbroath
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