Meanwhile Championship side Warrenpoint Town knocked out Ballinamallard
Linfield will travel to Institute in the sixth round of the Tennent's Irish Cup after beating Glentoran 2-1 in the Big Two clash on Saturday.
The tie in the north west is on February 4.
Championship side 'Stute had a 4-2 victory in their fifth round match away to Ballyclare Comrades.
The Drumahoe side are well-known to Linfield midfielder, Limavady man Steph
Lowry scored the first goal for the Blues on Saturday and was named man of the match.
Ex-Glens player Andy Waterworth got the extra-time winner at the Oval.
Manager David Healy's revealed he gambled by asking his top striker to play on with an injury - and it paid off...
Curtis Allen hit the goal of the game to put the Glens in front, curling a spectacular shot from 25 yards past former Northern Ireland keeper Roy Carroll...
Allen says the Glens still have plenty to play for this season - with a place in Europe at stake.
120 min: FT: Glentoran 1 - 2 Linfield. It's all over at the Oval and Andy Waterworth's extra time goal is enough to dispose of @Glentoran— Linfield FC (@OfficialBlues) January 7, 2017
Also in the next round of the cup...
Crusaders will play the PSNI at Seaview following a 2-0 win there on Saturday against Ards.
Cliftonville lost on penalties at Ballymena, who now face a trip to Harland and Wolff Welders.
Enjoy your evening Sky Blues. This season continues on in its now typical fashion.— Ballymena United FC (@BallymenaUnited) January 7, 2017
Thanks for support yet again.
There was more transfer window movement over the weekend in the city -
Glens midfielder Kym Nelson has joined the Reds on loan for the rest of the season.
And the Crues have added to their squad, bringing in defender Alan Keane, also to see out the current campaign.
The 32-year-old former Sligo player moves to Seaview after a spell with Dundalk.
Elsewhere in the cup, Championship leaders Warrenpoint had a penalty shoot-out victory against Premiership Ballinamallard and will host Mid-Ulster Intermediate League team Crewe United in the sixth round.
Here's the Point manager, former Linfield, Ballymena and Portadown striker, Matthew Tipton.
Coleraine will have home advantage against Tobermore after a 5-1 win over Carrick, with Eoin Bradley hitting a hat-trick on his return to the Showgrounds and Jordan Allan striking twice.
Meanwhile, the Bannsiders have completed the signing of 20-year-old midfielder Ciaron Harkin from Institute.
Dungannon Swifts - who beat Dergview 3-0 at Stangmore Park - will host another Mid-Ulster team, Dollingstown, in the cup next month.
Portadown had a 2-1 victory at Larne and manager Niall Currie will take the Ports to his old club, Loughgall.
Cup holders Glenavon recovered from 1-0 down to beat Portstewart 4-1 at Mourneview Park and will go to Armagh City in round six.
New signing James Gray scored twice for the Lurgan side.
Former Ex-Factor contestant, Eoghan Quigg, was included in the Portstewart line-up.
Tennent's Irish Cup sixth round draw
Saturday 4th February
Armagh City v Glenavon
Dungannon Swifts v Dollingstown
Crewe United v Warrenpoint Town
Coleraine v Tobermore United
Loughgall v Portadown
Institute v Linfield
HW Welders v Ballymena United
Crusaders v PSNI