Gerrard netted the second hat trick of his career on Jamie Carragher’s 500th appearance for the club – Carra was given a gaurd of honour as he took to the pitch and his son was mascot for the night.
Ryan Babel threatened several times but struggled to prove the killer pass or shot when out on the left side of midfield during the first half, but he broke the deadlock after switching to the right and from a Torres pass he hit across the keeper into the far corner.
BBC Sport Match Report
Steven Gerrard’s hat-trick sank Luton and lifted the spirits of embattled boss Liverpool Rafael Benitez.
Ryan Babel’s powerful finish broke the deadlock in first-half injury time, with Gerrard heading home from close range after 51 minutes.
Sami Hyypia turned in Gerrard’s corner six minutes later before the captain slid in his second from 14 yards.
Gerrard’s third came via a swerving shot to seal an FA Cup fourth round tie with Swansea or Havant & Waterlooville.
Both sides formed a guard of honour as Liverpool defender Jamie Carragher celebrated his 500th appearance for the club.
The Kop also cheered Benitez after revelations that American owners Tom Hicks and George Gillett had held secret talks with Jurgen Klinsmann to line him up as a potential successor to the Spaniard.
Luton fans were in good heart after administrator Brendan Guilfoyle revealed a deal has been agreed with a consortium, fronted by television presenter Nick Owen, to buy the club.
Liverpool, fielding a strong side including Gerrard and Torres, exerted total domination in the first 45 minutes.
But Luton, marshalled by former Anfield veteran Don Hutchison, defended heroically, putting their bodies on the line for a succession of brave blocks.
Peter Crouch should have done better than direct a fifth-minute header wide, and Babel curled a fine right-foot effort against an upright three minutes later.
Babel also had a shot deflected wide before he broke Luton’s brave.
Gerrard’s flick released Torres, and he set up the unmarked Babel for a drilled finish into the bottom corner past Dean Brill.
And Liverpool were home and dry after 51 minutes as Luton’s lack of height at the back was ruthlessly exposed.
Jermaine Pennant’s cross found Crouch at the far post and he knocked the ball into the path of the onrushing Gerrard, who headed beyond Brill.
Liverpool added a third six minutes later when Hyypia headed in Gerrard’s near post corner, via a deflection from Matthew Spring.
Gerrard added his second after 64 minutes, steering home a precise finish from 14 yards after Torres’ shot had been partially cleared into his path.
And a swerving long-range drive deceived Brill to complete Gerrard’s hat-trick after 71 minutes, leaving the captain to depart to a standing ovation from Anfield.
Match Reaction and Teams
“We weren’t really thinking about it because we know it’s important to progress in the FA Cup.
“I was not thinking too much about this, I was thinking about the game. I’m really happy because we won 5-0 and progressed in the competition.
“It wasn’t a bad week because we were training normally. We knew everyone was talking but we were trying to concentrate on the game against Luton. I know people must ask but I want to talk about the game.”
“They were square pegs in round holes but they gave me everything they have got.
“There is no doubt they (Liverpool) have ability in abundance and have done exceptionally well for Rafa.
“It was an awesome team they put out. Clearly they have done a great job for the manager.”
Liverpool: Itandje, Arbeloa, Carragher, Hyypia, Riise, Pennant, Alonso, Gerrard (Lucas 73), Babel, Crouch (Kuyt 65), Torres (Aurelio 73).
Subs Not Used: Martin, Kewell.
Goals: Babel 45, Gerrard 52, Hyypia 57, Gerrard 64, 72.
Luton: Brill, Jackson, Hutchison, Keane, Goodall, Bell (McVeigh 73), Robinson (O’Leary 68), Spring, Currie, Andrew (Furlong 68), Talbot.
Subs Not Used: Parkin, Emanuel.
Ref: Peter Walton (Northamptonshire)