The Glens and St Patrick's Athletic had drawn 0-0 in the first leg and it was another close affair with Martin Murray eventually grabbing the all important goal on 62 minutes.
Coleraine, who held a 1-0 lead from the first leg, were knocked out by the last kick of the game when Ciaran Kilduff scored from close in to make it 2-0 on the night for Shamrock Rovers and 2-1 on aggregate. Mark Quigley had earlier tied the scores on the night with a sixth minute opener.
In the first leg of the Drogheda match against Portadown it saw five goals with the League of Ireland side edging it 3-2 but any hopes Ronnie McFall's men had of progressing vanished in the first half as United built up a 2-0 lead thanks to strikes from Alan Byrne on just 52 seconds and Paul O'Connor (12).
Three more goals from Gavin Brennan (55), David Cassidy (78) and Philip Hand (90) gave Drogheda a 5-0 win on what was a miserable night for the Ports.
Cliftonville, 4-0 down from the first leg, had an almost impossible task to see off Cork City but they did produced a much better performance with the match ending 2-2 at Solitude.
Daryl Horgan gave the visitors the lead on 15 minutes but this was cancelled out by Liam Boyce on 38 minutes.
Cork hit the front again seven minutes into the second half but the Reds battled right to the end and were rewarded when Stephen Garrett fired home three minutes from time. Cork's Kalin Spillane was sent off on 90 minutes.
Tuesday's Setanta Cup Results:
- Glentoran 1 - 0 St Patrick's Athletic
- Coleraine 0 -2 Shamrock Rovers (1-2 on aggregate)
- Drogheda 5-0 Portadown
- Cliftonville 2-2 Cork City
Setanta Cup Quarter-Finals Draw:
First leg matches:
- Cork City v Crusaders (Tuesday 26 February)
- Sligo Rovers v Glentoran (Monday 4 March)
- Derry City v Drogheda United (Monday 4 March)
- Shamrock Rovers v Linfield (Monday 4 March)
Second leg matches:
- Crusaders v Cork City (Monday 4 March)
- Glentoran v Sligo Rovers (Monday 11 March)
- Drogheda United v Derry City (Monday 11 March)
- Linfield v Shamrock Rovers (Monday 11 March)