Cliftonville started their bid for a fourth straight League Cup success by beating Championship side Dundela 2-1 in the second-round game at Solitude.
David McDaid slotted in a penalty after he was fouled and the Reds striker doubled the lead on 55 minutes.
Martin Murray's own goal gave the Duns hope but the holders progressed.
Andrew Mitchell's double helped Dungannon to a 3-0 win over Newington YC while Stephen Murray bagged a treble as Warrenpoint beat Distillery 5-1.
Mark McClelland's foul on McDaid set the Reds on their way to victory in north Belfast, with the spot-kick converted by the former Derry City forward.
Fra Brennan, Murray and Stephen Garrett went close for the hosts before McDaid made it 2-0, slotting in from Johnny Murray's low ball across the box.
Adam Neale headed over for Dundela and they pulled one back nine minutes from time back when Murray over-hit a backpass into his own net.
Murray fired wide as he attempted to make amends and, despite a sluggish performance, Tommy Breslin's side secured a deserved win.
Jamie Glackin set up Ally Teggart to score a fourth minute opener for Dungannon Swifts in their Seaview clash with Newington.
Swifts keeper Johnny Addis denied Padraig Scollay before Mitchell blasted over when clear through.
Mitchell headed in twice within four minutes midway through the second half to seal victory.
Mikey Withers equalised for the Whites after an early Stephen Hughes goal at Milltown but Warrenpoint held a 2-1 lead at half-time thanks to Murray's header.
The hosts dominated the second half with substitute Mark McCabe heading home before Murray struck twice in added time.