It took just seven minutes for the rampant Blues to find the net, with Peter Thompson heading in the opener.
Mark McAllister doubled his side's advantage when he finished from close-range in the 21st minute, and Michael Carville made it 3-0 with a fine finish from the edge of the penalty area into the top corner right from the restart.
Thompson struck with another header after 27 minutes, and completed his hat-trick before the break when he pounced on a loose ball inside the area.
David Jeffrey's side took their foot off the gas somewhat in the second half, but Jamie Mulgrew added a sixth nine minutes from time before Thompson grabbed his fourth of the afternoon from the penalty spot to wrap up an emphatic win that keeps Linfield on course to claim the league and cup double for the second successive season.
Away from the Oval there were five games in the Carling Premiership on Saturday, with Glentoran ending a seven-game winless streak against Portadown at Shamrock Park.
Leon Knight grabbed the crucial goal with a fine solo effort seven minutes into the second half to wrap up a 1-0 win for Eddie Patterson's side.
In the other game in the top half of the table Cliftonville and Crusaders drew 1-1 at Solitude.
Cliftonville edged a scoreless first half, but had to wait until the 83rd minute to break the deadlock, when George McMullan scored from the spot after Joe Gormley had been fouled in the area.
However, Crusaders hit back with a headed goal from Michael Halliday in injury time to ensure a share of the spoils.
In the bottom half Carrick Rangers appear doomed to relegation after they fell to a 3-0 defeat to Ballymena United at the Ballymena Showgrounds.
James Costello claimed the match ball by scoring all three goals, with the first coming on the half hour.
The striker added a second seven minutes after the restart, and completed the hat-trick when he latched onto an Alan Teggart cut-back two minutes from time.
Glenavon meanwhile looked to have edged away from the threat of relegation after a convincing 4-0 victory over Donegal Celtic in an incident-packed game at Mourneview Park.
The opening goal came in the 11th minute when Gary Hamilton's corner caused havoc in the Belfast Hoops' defence, and Jay Magee bundled the ball over the line.
Brian McCaul made it 2-0 with a penalty five minutes later after Tony Grant was fouled by Darren McNamee, and Ciaran Doherty added a third with a headed effort a minute before the break.
DC were reduced to ten men when Paul Bradley was sent off for a second booking after an ugly challenge on McCaul inside the box, but Glenavon player-manager Gary Hamilton was left red-faced when his cheeky chipped spot-kick was read - and saved - by DC keeper Gerard McVeigh.
Mark Miskimmin did add a fourth goal when he blasted home in the 79th minute, and DC's misery was complete when they lost Declan O'Hara to a straight red two minutes from time.
In the game at Stangmore Park Dungannon Swifts came back from two goals down to secure a 3-2 victory over Lisburn Distillery.
Gary Thompson gave the visitors an early lead when he volleyed home in the second minute, and he added another in the ninth minute when he knocked in the rebound after Niall Morgan failed to hold David Cushley's free kick.
However Michael McKerr reduced the deficit with a goal in the 29th minute, and it was all-square just before the end of the half when Ryan O'Neill finished from a Johnny Topley cross.
The winner came right at the death when Ryan Harpur got on the end of a free kick deep in added time.
Irish Cup semi-final:
Linfield 7 - 0 Newry City
Linfield: Thompson 7, 27, 39, 82 (pen); McAllister 21, Carvill 23, Mulgrew 80.
Ballymena Utd 3 - 0 Carrick Rangers
Ballymena Utd: Costello 29,56,85.
Cliftonville 1 - 1 Crusaders
Cliftonville: McMullan 83 (pen).
Crusaders: McCreadie 90.
Dungannon Swifts 3 - 2 Lisburn Distillery
Dungannon Swifts: McKerr 29, O'Neill 43, Harpur 90+2
Lisburn Distillery: G Thompson 7,9
Glenavon 4 - 0 Donegal Celtic
Glenavon: Jay Magee 11, McCaul 16 (pen), Doherty 44, Miskimmin 79.
Portadown 0 - 1 Glentoran
Glentoran: Knight 52.