Crusaders began their defence of the League Cup with a comfortable 3-0 win over Glebe Rangers at Seaview.
Gary McCutcheon scored a first-half penalty, while Timmy Adamson and Matthew Snoddy added second-half goals.
H&W Welders caused an upset at Suffolk Road by coming from behind to beat Donegal Celtic 2-1, Nathan McConnell and Curtis Black with the vital goals.
Premiership clubs Ballinamallard, Ballymena, Cliftonville and Coleraine all progressed on 4-1 scorelines.
Paul McVeigh had given DC a 37th-minute lead but the Welders scored twice in the last 10 minutes to clinch victory.
Glebe Rangers had Jackie Morrison sent-off on 47 minutes for a second yellow card offence.
Ballymena led Lurgan Celtic 1-0 at half-time thanks to a confident finish by Neil Lowry and Gary Thompson then scored his first goal for the club with a fine low drive in off the far post.
Allan Jenkins grabbed the third from the edge of the box and James McCabe added the fourth.
Stefan Campbell netted for Lurgan Celtic.
Darren Boyce gave last year's beaten finalists Coleraine an early lead at Ballymoney and further goals by Mark Gillan, a Curtis Allen penalty and a second-half strike by Ruairi Harkin saw them comfortably into the draw for the next round.
Stephen Lyons found the net for the home side.
Cliftonville were level at 1-1 at half-time against Tobermore United at Solitude after Marc Smyth gave the Reds the lead and Stephen Murray equalised.
Goals by Stephen Garrett (67) and a Joe Gormley double on 68 and 80 minutes completed a convincing win for Tommy Breslin's side.
At Ferney Park, a Ryan Campbell goal gave Ballinamallard the lead, but Kevin O'Neill levelled for Knockbreda Parish before half-time.
Chris Curran nudged the Premiership newcomers in front with a brilliant strike on 48 minutes, before Campbell grabbed his second and James McKenna completed the scoring.
At Newry, Philip Donnelly found the net in the eighth minute for the home side but second-half goals by Conor Carlin and Liam McMenamin saw Dergview go through.
Bangor earned their place in the hat thanks to goals by Dean Youle, Gareth McLaughlin, Ryan Murray and Sean Cahill.
Stephen Murray scored twice for their opponents Armagh City.
IRN-BRU League Cup second round results
Ballinamallard United 4-1 Knockbreda Parish
Ballymena Utd 4-1 Lurgan Celtic
Ballymoney Utd 1-4 Coleraine
Bangor 4-2 Armagh City
Cliftonville 4-1 Tobermore Utd
Crusaders 3-0 Glebe Rangers
Dergview 2-1 Newry City
Donegal Celtic 1-2 H&W Welders
Dungannon Swifts 2-2 Coagh Utd (AET) - Coagh win 7-6 on penalties
Glenavon 6-1 Sport & Leisure
Glentoran 3-1 PSNI
Institute 1-0 Banbridge Town
Killymoon Rangers 0-5 Carrick Rangers
Limavady Utd 1-3 Lisburn Distillery
Linfield 3-1 Ards
Portadown 3-0 Dundela