Holders Celtic will host promoted Falkirk in the Premier Sports Cup, while third-tier Alloa Athletic's reward for topping their group is a visit to Rangers following the draw for the last 16.
The draw was made after St Mirren beat Ayr United 2-1 to secure the final spot for group winners and Stephen Robinson's side will host Scottish Premiership rivals Heart of Midlothian.
Despite defeat, Ayr edged out Dunfermline Athletic as one of the three best runners-up and Scott Brown's side will visit Championship rivals Partick Thistle.
Aberdeen, Dundee United and Hibernian, along with Celtic and Rangers, had received byes to the second round because of their participation in European competitions.
The Dons have been drawn away to Championship side Greenock Morton, while United and Hibs will visit Premiership opposition in the shape of Kilmarnock and promoted Livingston respectively.
Relegated St Johnstone host top-flight Motherwell in the remaining tie, with matches to be played on 16/17 August.