The Bairns finished second behind Dunfermline with three wins from their four group matches, and will welcome the Gers as they bid to make the quarter-finals.
Celtic, meanwhile, were handed a home tie against Ross County while Hearts face a trip to Championship rivals Alloa Athletic.
Hibs and Dundee were drawn to face each other less than an hour after the two teams had faced off in the final Group B match at Easter Road.
In the other ties, Aberdeen travel to Paisley to face St Mirren while Livingston host Ayr United.
There was one other all-Championship clash with Arbroath being drawn at home against Dunfermline Athletic while Motherwell and St Johnstone will meet at Fir Park in the third all-Premiership affair.
The matches will be played on the weekend of November 28 and 29.