CORK City completed the job with a draw at Solitude.
Ahead firstly through Daryl Horgan and then Danny Furlong, the Leesiders – who finished the contest with 10 men – were twice pegged back, but never looked likely to ship the avalanche of goals the Belfast side required to turn the tie on its head.
Having fielded a virtual reserve side at Turner's Cross last time out, the hosts made no fewer than eight changes to their line-up. Cliftonville's goals came courtesy of Liam Boyce and Stephen Garrett.
Cork's progress was soured somewhat when Kalen Spillane received a straight red card from referee Ross Dunlop after appearing to aim an elbow in the direction of Marc Smyth as the duo tussled for an aerial ball in injury-time but, that black mark aside, boss Tommy Dunne will have been delighted.
CLIFTONVILLE – Devlin, R Scannell, Johnston (Donnelly 65), McMullan, Garrett, O'Carroll (Caldwell 65), Seydak, Smyth, Gormley, Knowles, Boyce (Cosgrove 75).
CORK CITY – McNulty, Turner, Murphy, Murray, G Morrissey, Duggan, Kavanagh (Behan 74), Furlong D Morrissey 62), Spillane, N Horgan, D Horgan (Rundle 81).
REF – Ross Dunlop
REFEREE: Ross Dunlop
Boyce levelled on the night after bundling his way past a brace of challenges inside the area.
The hosts began the second-half brightly but, just like before, saw a series of half-chances come and go before Cork pounced to restore their lead in clinical fashion when the lively Daryl Horgan sprung Cliftonville's offside trap to tee Furlong up for a strike he simply couldn't miss.
Cliftonville virtually dominated proceedings thereafter but never looked likely to net the six goals required to sneak a quarter-final berth, with Neal Horgan and Daryl Kavanagh producing timely blocks to keep Martin Donnelly and Garrett at bay.
Mark McNulty made a superb point-blank save to repel George McMullan's header but the keeper was beaten with two minutes to play when Garrett raced clear of Murray to clip home and level things on the night.
Cork's progress was soured somewhat when Kalen Spillane received a straight red card from referee Ross Dunlop after appearing to aim an elbow in the direction of Marc Smyth as the duo tussled for an aerial ball in injury-time but, that black mark aside, boss Dunne will have been delighted to complete the job and ensure progress against the Irish League's champions in waiting.
CLIFTONVILLE: Devlin, R Scannell, Johnston, McMullan, Garrett, O'Carroll, Seydak, Smyth, Gormley, Knowles, Boyce. Subs: Brown, Donaghy, Caldwell (for O'Carroll, 65 mins), Donnelly (for Johnston, 65 mins), Lynch, Cosgrove (for Boyce, 75 mins), McVeigh.
CORK: McNulty, Turner, Murphy, Murray, G Morrissey, Duggan, Kavanagh, Furlong, Spillane, N Horgan, D Horgan. Subs: Behan (for Kavanagh, 74 mins), Rundle (for D Horgan, 81 mins), D Morrissey (for Furlong, 62 mins), Kenny, Burns, Buckley, Abbott.
REFEREE: Ross Dunlop (Carrickfergus)