The Terrors lost on penalties to eventual winners Celtic in the last-four clash at Hampden in January.
Following Tuesday's draw, they start this year's campaign with a trip to Recreation Park to face the Second Division Wasps.
St Johnstone and St Mirren were emphatic winners in the first-round ties and are rewarded for their progress with trips to Arbroath and Ayr United respectively.
Hibernian - trophy winners in 2007 - will host Brechin, Hamilton are away to Ross County and Kilmarnock entertain Morton.
The ties will be played on Tuesday August 25 and Wednesday August 26.
Co-operative Insurance Cup second-round draw: Inverness Caledonian Thistle v Albion Rovers, Forfar Athletic v Dundee, Dunfermline Athletic v Raith Rovers, Arbroath v St. Johnstone, Partick Thistle v Queen of the South, Alloa Athletic v Dundee United, Hibernian v Brechin City, Ross County v Hamilton Academical, Kilmarnock v Morton, Ayr United v St. Mirren.
Source: Team_Talk