Conor Bradley was the star of the show as the 20-year-old right-back scored and teed up goals for Diogo Jota and Dominik Szoboszlai.
Christopher Nkunku reduced Chelsea’s arrears, but Luis Diaz rounded off the scoring and a thrilling Liverpool performance.
Indeed, the scoreline flattered the visitors as Darwin Nunez hit the woodwork four times, including from the penalty spot in the first half.
“We could have scored and should have scored more goals. You cannot score five, six goals against Chelsea if you are not outstanding,” said Klopp.
Victory restores a five-point lead at the top of the table for Klopp’s men over Manchester City, who have a game in hand, and Arsenal. The Gunners face Liverpool on Sunday.
Klopp had called for the news of his impending departure at the end of the season not to be a distraction and on this evidence it may only provide more inspiration for his side to deliver just a second league title in 34 years.
Once again the injured Mohamed Salah was not missed as Jota and Nunez provided a constant threat, while Bradley’s emergence is blocking Trent Alexander-Arnold’s return to the starting line-up.
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Nunez had five shots inside the first 18 minutes as a combination of Djordje Petrovic and the woodwork on two occasions kept the Uruguayan at bay.
Jota was not so forgiving when he carved through the heart of the Chelsea defence to slam home on 23 minutes.
‘Wonderful kid’
Bradley has been a revelation since a knee injury to Alexander-Arnold opened his path to the first team.
The Northern Irishman produced a finish that Alexander-Arnold would have been proud of as he burst down the right and fired low and hard into the far corner to double Liverpool’s lead.
“What a wonderful kid he is. Outstanding finish, the whole game, the contribution, the involvement,” said Klopp of Bradley.
“I’m really happy for him. He’s a very serious young man and that was pretty special I have to say.”
Defeat leaves Chelsea still down in 10th and now 20 points adrift of Liverpool.
Mauricio Pochettino admitted his side need to be much better to stand any chance when the sides meet again in the League Cup final on February 25.
“Being honest we didn’t perform the way we wanted to perform,” said Pochettino. “They were better than us during 90 minutes.
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“You have to say ‘well done to Liverpool’. If you want to match them in the final, we need to compete in a different way.”
Chelsea were handed a brief reprieve when Nunez hit the post from the spot after Jota had been stood on by Benoit Badiashile.
But Liverpool’s third did not take long to arrive after the break as another purposeful run and pinpoint cross from Bradley picked out Szoboszlai to head home.
Klopp could then afford the luxury of making a quadruple substitution as Alexander-Arnold and Andy Robertson stepped up their comeback from injuries.
The changes briefly knocked the hosts out of their stride as Chelsea grabbed a consolation.
Nkunku’s debut season in England has been ravaged by injury but the Frenchman now has two Premier League goals in less than 180 minutes on the pitch as he finished smartly into the far corner.
Nunez’s frustrating night in front of goal went on as he then headed against the crossbar to become the first Premier League player to hit the woodwork four times in a match.
But he still had a major role to play in Liverpool’s fourth as Diaz burst onto his driven cross to erase any possibility of a Chelsea revival.
Liverpool thrash sorry Chelsea to stretch Premier League lead