Ballyclare Comrades's reward for their shock League Cup win over Linfield will be a third-round tie against Ballymena United at the Showgrounds.
The draw produced three all-Premiership tries with Glenavon hosting Glentoran, Crusaders at home to Coleraine and Institute taking on Ballinamallard.
Holders Cliftonville have been handed a trip to Carrick Rangers.
The other ties will see Ards facing Dungannon, H&W Welders against Bangor and Knockbreda against Portadown.
The third-round ties will take place on Tuesday, 7 October.
Wasp Solutions League Cup third-round draw
Ards v Dungannon Swifts
H&W Welders v Bangor
Knockbreda v Portadown
Crusaders v Coleraine
Institute v Ballinamallard United
Carrick Rangers v Cliftonville
Glenavon v Glentoran
Ballymena United v Ballyclare Comrades