The Reds were rampant after the break and their pressure paid off when captain Virgil van Dijk showed desire and determination to get his side on level terms by powering home a header from a 56th-minute corner.

Just 125 seconds later Liverpool led as Cody Gakpo nodded in from close range as Alexis Mac Allister fired in a cross from the byeline.

Diaz, with his ninth shot of the game, finally got his reward for relentless work with the third goal in the 71st minute.

The Colombian forward danced his way into the box and coolly side-footed beyond Thomas Kaminski at the near post to give the hosts some breathing space on what had initially looked like a night when they could slip up in the title race.

Harvey Elliott, making his 100th appearance for the club, rounded off a fine second half when he pounced on a loose ball in the 90th minute to claim the fourth.

It made it three wins on the bounce for Liverpool after losing 3-1 at Arsenal last month and built further momentum as they gear up for Sunday's EFL Cup final against Chelsea at Wembley.

Jurgen Klopp's men boast a four-point cushion over second-placed Manchester City, although they have played a game more than the defending champions, while Luton remain third from bottom.

Resilient Reds show strength in depth

With nine senior players unavailable due to injury, including goalkeeper Alisson, Mohamed Salah, Trent Alexander-Arnold, Darwin Nunez and Dominik Szoboszlai, manager Klopp had no other option than to trust the depth of his squad.

He named a starting line-up with an average age of 25 years and 68 days - the club's youngest since February 2018 - while Liverpool's bench had five players aged 19 or under, with 16-year-old midfielder Trey Nyoni among the substitutes.

With the EFL Cup final next up, Liverpool could have been excused for having their minds elsewhere and that's certainly how it looked in the opening 45 minutes as they were wasteful in front of goal.

Klopp's face told a story as his side emerged from the tunnel for the second half.

Whatever he said to his players clearly had the desired impact as they came out of the blocks with intent and got the job done in style to extend their unbeaten home league run to 25 games.

The German said in his pre-game programme notes Liverpool could not afford to "feel sorry for ourselves" as they deal with a lengthy injury list and he stressed the importance of "living in the moment" as they continue to fight for silverware on four fronts.

They now head south in buoyant mood, bidding for a seventh major trophy under Klopp.

Key fixtures on horizon for Hatters

Following this latest loss, Luton have not won a league game at Anfield in 15 attempts, but they have come a long way since their last visit in January 2008, when they lost 5-0 in an FA Cup third-round replay.

Luton were in League One on that day, 61 places below their hosts in the football ladder and having just discovered they had been saved from administration. Since that trip, the Hatters have dropped out of the Football League altogether and worked their way back up to the top flight.

Ogbene's 12th-minute effort, Luton's first at Anfield since 1992, came very much against the run of play as Tahith Chong's shot deflected invitingly into his path off goalkeeper Caoimhin Kelleher.

However, Luton lacked presence in the final third without the injured Elijah Adebayo, when they did manage to get forward after getting their noses in front.

Ultimately, Liverpool's unwillingness to let this game get away from them proved too much for them to handle as they folded and fell to a third successive defeat.

While boss Rob Edwards may not have marked this game as a big opportunity to get three points at the start of the season, he will have had his eyes firmly fixed on matches to follow next month.

They host Manchester City in the FA Cup fifth round on Tuesday before Luton embark on a run which could define their league campaign.

Aston Villa travel to Kenilworth Road on 2 March and then they face three clubs currently sitting in the bottom eight - Crystal Palace, Bournemouth and Nottingham Forest.