Rangers will start their attempt to retain the Scottish League Cup with a third round tie against First Division club Dunfermline at Ibrox.
Walter Smith's Scottish champions defeated St Mirren 1-0 in the final at Hampden Park in March and will expect to progress to the latter stages again.
Celtic have been drawn at home against Inverness Caledonian Thistle, who they beat 1-0 on the opening day of the Scottish Premier League season. In another all-top flight clash, Hibernian travel to Kilmarnock.
Aberdeen will have revenge on their minds when they face First Division side Raith at Pittodrie after being knocked out of the Scottish Cup by Rovers last season.
Dundee United face Ross County in a repeat of last season's Scottish Cup final.