Holders Linfield progressed to the last eight of the BetMcLean Cup as goals by Joel Cooper in either half helped them see off Glentoran 2-1 at the Oval.
Championship side Portadown were 2-1 winners over Crusaders thanks to Kenny Kane and Eamon Fyfe strikes.
Matt Lusty's second-half goal saw Dungannon Swifts past Cliftonville 1-0.
Larne beat Ards 5-3 after extra-time, Coleraine edged out Ballymena United 18-17 on penalties and Newry City beat Carrick Rangers 3-1 in a shootout.
Ballymena had led at half-time against Coleraine thanks to Scot Whiteside's header but Josh Carson's penalty left it 1-1 at full-time and after extra-time.
Home goalkeeper Sam Johnston missed what turned out to be the decisive attempt from the spot after a marathon shootout on Warden Street which eventually concluded at 22:50 GMT after 44 penalties.
The game between Newry City and Carrick had ended 2-2, leaving the two Premiership teams to decide their contest on penalties.
The scheduled tie between Limavady United and Glenavon at Limavady Showgrounds was postponed because of a floodlight failure at the Limavady Showgrounds.
Cooper shines for Linfield
At the Oval, Linfield took the lead after 14 minutes when Chris Shields crossed from the left and Cooper was afforded too much time to bring the ball down and slot home beyond a helpless Aaron McCarey.
Linfield doubled their lead two minutes into the second half as Cooper superbly curled home from the edge of the box into the top left-hand corner following Jonathan Russell's attempted headed clearance.
Seven minutes from time and Glentoran had a lifeline. Daire O'Connor's cross was met with a powerful header by Jay Donnelly, who found the top corner of the net.
Linfield's victory makes it 10 wins in a row in all competitions for David Healy's side, while Glentoran are without a win in their last three outings.
Ports stun Crues
Portadown, who sit second in the Championship table, were quickly out of the blocks as Kane put them in front in the 11th minute.
The former Ballymena striker was left through on goal after Joshua Robinson misjudged Aaron Traynor's attempted pass, then made his way into the box before firing a strong strike into the bottom corner.
Niall Currie's men nearly doubled their lead shortly after when Ryan Mayse connected with Traynor's looping cross and fired a well-struck effort towards goal, which forced Jonathan Tuffey into a fine save.
The visitors levelled the tie midway through the first half when Lloyd Anderson dribbled towards the box, with the on-rushing Aaron Hogg coming to the edge of the box to try clear the danger.
The Portadown stopper originally saved his resulting strike but spilled the ball, with Anderson skilfully passing to Mikhail Kennedy, whose drilled effort from the edge of the box found the back of the net.
The home side's winner came in the 74th minute when Fyfe latched onto the ball inside the box and coolly fired his strike between the legs of Tuffey.
Swifts too strong for Reds
2018 winners Dungannon Swifts booked their place in the quarter-finals of this year's competition with an impressive 1-0 over Cliftonville at Stangmore Park.
Lusty's third goal of the competition was enough to separate the two when the Larne loanee evaded Luke Kenny's challenge before firing past Nathan Gartside's near post.
The Swifts had dominated proceedings in the first half with several chances to take the lead with Ethan McGee, Kealan Dillon and Lusty all going close.
Cliftonville improved in the second half and had chances to take the lead, with the biggest falling to Ronan Hale. Jonny Addis found the run of the former Larne striker, but with only Declan Dunne to beat, Hale blazed his effort over from close range.
The Swifts continued to look dangerous going forward and could have taken the lead earlier when Caolan Marron struck the outside of the post from inside the Cliftonville penalty area. Lusty's goal subsequently settled the tie however.
Bannsiders advance after mammoth shootout
Coleraine defeated Ballymena United 18-17 in an extraordinary penalty shootout as they continue their bid to reach a fourth consecutive final.
The home side grabbed the lead a minute before the break when Steven McCullough's free kick was met with a powerful downward header from skipper Whiteside.
Coleraine levelled on 58 minutes when Mikey Place brought down substitute David McDaid and Carson smashed the resultant penalty straight up the middle.
Isaac Westendorf had the best chance to win it for Ballymena in normal time when he burst into the Coleraine penalty area but with team-mates better placed, he went for goal himself and Deane was able to block his effort.
In two tense periods of extra time, McDaid's goalbound shot was brilliantly blocked by Ballymena defender Corrie Burns, while Michael McCrudden had a header ruled out for offside.
In a chaotic penalty shootout, the visitors eventually prevailed by an 18-17 scoreline after 44 penalties.
Larne and Newry through
Larne survived a scare at Bangor, before eventually prevailing in an eight-goal thriller against Championship outfit Ards after an additional 30 minutes.
Callum Dougan had Ards ahead, but Seam Graham and Andy Ryan were on target as the Premiership champions went in one goal to the good at the interval.
Ross Hunter restored parity before Paul O'Neill put Larne in front again, before Connor Maxwell made it 3-3 to take the game to extra-time.
Further goals from lee Bonis and O'Neill ensured passage from the last 16 for Tiernan Lynch's charges.
A Ciaran O'Connor penalty made it 1-0 to Newry against Carrick at the Loughview Leisure Arena, only for Kyle Cherry to equalise after half-time.
Reece Glendinning's goal handed Carrick the advantage but Adam Salley levelled, before Newry came out on top in the shootout.