Holders Coleraine plus Ballymena United, Cliftonville and Warrenpoint Town make up the BetMcLean League Cup semi-finals line-up following last eight victories over Glentoran, Linfield, Portadown and Limavady United respectively.
The Bannsiders continued their cup defence at The Showgrounds thanks to a goal in each half from Jamie Glackin and Matthew Shevlin.
Glackin opened the scoring on 19 minutes after combining in a one-two with Conor McKendry, with Shevlin adding a second just after the hour when he pounced on a mistake by Malachy Smith before finishing confidently past Glentoran keeper Ross Glendinning.
Ballymena United came from a goal down to defeat Linfield 3-1 at Warden Street.
Billy Chadwick fired the Blues in front after eight minutes, a lead they held until the 37th minute when Douglas Wilson levelled with a header from Ross Redman's corner.
Jude Winchester made it 2-1 nine minutes into the second half with a low finish after Shields failed to cut out a Kenny Kane ball before, deep into stoppage time, Leroy Millar added a third on the counter attack.
Cliftonville and Portadown needed extra-time at Shamrock Park before the visitors came out on top through a 97th minute Daniel Kearns finish.
Portadown had moved in front through Lee Bonis on 47 minutes but Ronan Doherty levelled for the league leaders with around a quarter-of-an-hour of normal time remaining.
Meanwhile, at Milltown, Alan O'Sullivan bagged a hat-trick as Warrenpoint Town swept past Premier Intermediate League opponents Limavady United.
He opened the scoring after just two minutes before Thomas Maguire added another soon after. O'Sullivan made it 3-0 on 25 minutes, Stuart Hutchinson grabbed a fourth after half-an-hour with Maguire doubling his own tally just before the break.
O'Sullivan then completed his hat-trick from the spot on 53 minutes with the Roesiders getting a consolation late on through Matthew Brown.