The Irish Premiership overcome their Championship opponents through an Adam Brown volley.
- Holders Crusaders start with a win over Knockbreda
- Linfield, Glentoran, Cliftonville, Ards, Larne and Ballyclare also through to quarter-finals
- Ballymena United take on H&W Welders in final tie on Wednesday
Adam McCart and Joe Tully hit the Newington net in the second period of extra-time to put Ballyclare through to the quarter-finals.
Newington levelled after Jamie Willighan gave the home side an early lead.
Tommy Stewart puts Larne 2-0 up in the 49th minute with his second of the game when he pounced to score the rebound after Liam McCauley had saved Ben Tilney's shot.
Tommy Stewart had earlier headed home a Graham Kelly cross in the 42nd minute to give Larne the lead.
The Reds secure a comfortable win at Solitude with Ryan Curran Curran adding a late fifth after Joe Gormley hit a second-half double.
Cliftonville scored twice in three minutes midway through the first half with Ryan Catney firing home off the post before Jay Donnelly doubled the lead.
The holders are through to the quarter-finals with Rodney Brown heading in the winner from a corner seven minutes into the second half.
Gary Thompson put the holders in front on 19 minutes with a follow-up finish after Rory Patterson's shot was kept out by keeper Dean Smyth.
Championship side Knockbreda equalised after 35 minutes with Brendan Bennett smashing past Harry Doherty from 10 yards,
The Glens come from behind to secure a place in the last eight.
Curtis Allen scored twice in the second half for the hosts after Queen's took a surprise lead on the stoke of half-time with Chris Middleton netting his first Queen's goal.
The Blues will meet Belfast rivals Glentoran in the quarter-finals after defeating PSNI.
Jimmy Callacher connected with a Niall Quinn corner after 71 minutes to restore Linfield's lead at Windsor Park.
Mark Anderson hit a PSNI leveller five minutes before the break after Mark Stafford headed the Blues in front.