Chelsea’s surprise defeat at home to Fulham earlier in the day had been an unexpected gift for Arne Slot’s side and they drove home their advantage by outclassing the struggling Foxes.
Having overcome the early setback of conceding to Jordan Ayew, with even the travelling fans expressing their surprise they were winning away after taking just five points on the road this season, the home team had too much quality.
That was personified by the excellent Cody Gakpo, whose eighth goal in his last 14 appearances produced the equaliser in first-half added time with the Netherlands international unlucky to have a second ruled out for offside by VAR.
Further goals from Curtis Jones and Mohamed Salah, with his 19th of the season, stretched Liverpool’s unbeaten run to 22 matches.
For Leicester, who had slipped into the bottom three after Wolves’ win over Manchester United, it is now one win from the last 10 in the league and Ruud van Nistelrooy has plenty of work to do, although he was not helped here by the absence of leading scorer Jamie Vardy through injury.
It looked liked Liverpool meant business from the off with Salah’s volley from Gakpo’s far-post cross just being kept out by Jakub Stolarczyk, making his league debut after former Liverpool goalkeeper Danny Ward was omitted from the squad having struggled in the defeat to Wolves.
But if the hosts thought that had set the tone they were badly mistaken after being opened up with such simplicity in only the sixth minute.
Stephy Mavididi broke down the left and his low cross picked out Ayew, who turned Andy Robertson far too easily, with his shot deflecting off Virgil van Dijk to take it just out of Alisson Becker’s reach.
With a surprise lead to cling to Leicester knew they had to quell the storm heading their way and they began by trying to take as much time out of the game as they could, much to Anfield’s frustration.
It took a further 18 minutes for Liverpool to threaten with Gakpo cutting in from the left to fire over, a precursor for what was to follow just before half-time.
That was the prompt for the attacks to rain down on the Foxes goal, with Salah’s shot looping up off Victor Kristiansen and landing on the roof of the net and Robertson heading against a post.
Gakpo’s inclination to come in off the left was proving a problem for the visitors, doing their utmost to resist the pressure, but when Salah curled a shot onto the crossbar on the stroke of half-time it appeared they had survived.
However, Gakpo once again drifted in off the flank to collect an Alexis Mac Allister pass before curling what is fast becoming his trademark effort over Stolarczyk and inside the far post.
Early the second half Darwin Nunez fired over Ryan Gravenberch’s cross before Jones side-footed home Mac Allister’s cross after an intricate passing move inside the penalty area involving Nunez, Salah and the Argentina international.
Leicester’s ambition remained limited but Patson Daka should have done better from a two-on-one counter attack with Mavididi but completely missed his kick with the goal looming.
Nunez forced a save out of the goalkeeper before Gakpo blasted home what he thought was his second only for VAR to rule Nunez was offside in the build-up.
But Liverpool’s third was eventually delivered by the left foot of Salah, who curled the ball outside Kristiansen, inside Jannick Vestergaard and past Stolarczyk inside the far post.
