Richarlisons early goal and Gylfi Sigurdssons late penalty secured the derby spoils for Carlo Ancelottis side.
Everton ended their 22-year wait for a Merseyside derby win at Anfield with a 2-0 victory which consigned Liverpool to their worst home league run in almost a century.
There were echoes of Kevin Campbell’s early goal in 1999 when Richarlison scored in just the third minute and if there is one thing Italian manager Carlo Ancelotti knows what to do well it is setting up sides to hold onto leads.
Despite coming under mounting pressure the visitors held out and hit their hosts with an 83rd-minute sucker punch via Gylfi Sigurdsson’s penalty.
Victory, their first in 23 derbies, saw Everton draw level on 40 points with their seventh-placed hosts but with a match in hand.
The last time Liverpool lost four in a row at home was 1923 and just when they thought their season could not get any worse with defeat to their neighbours for the first time this millennium, they lost yet another centre-back option as Jordan Henderson became the fifth no longer fit for duty.
October’s derby was the start of their defensive problems when Virgil Van Dijk was ruled out for the season with an ACL injury after a reckless tackle by Everton goalkeeper Jordan Pickford but there was no such controversy this time.
Henderson’s problem appeared to be a groin injury as he pulled up running the ball out of defence in the first half, leaving his side with an 18th different – and most inexperienced – pairing of Ozan Kabak and substitute Nat Phillips.
But by then the damage had already been done as Everton had made their intent clear as, straight from kick-off, the ball was lumped forward and under no pressure Kabak conceded a corner after six seconds.
The on-loan Schalke defender, in only his third appearance, was immediately targeted by Richarlison as the Brazil international attached himself to the 20-year-old.
It paid off after just three minutes as two weak headers, one from Thiago Alcantara and another from Kabak on his Anfield debut, saw the ball fall to James Rodriguez and he slipped in a pass behind the new boy for Richarlison to run onto and fire an angled drive across Alisson Becker.
The Brazilian is only the third Everton player to score in back-to-back Premier League appearances at Anfield after Tim Cahill (2006) and Campbell (2000).
He also gave the visitors their first lead in a derby since October 2010, the date of their last victory which came at Goodison Park.
Kabak’s edgy nerves were not eased when he allowed a Pickford clearance to drop over his head straight to the feet of Richarlison, before moments later clattering Rodriguez after a mistimed challenge and he finished the half with a booking – for the third successive match – to cap a poor 45 minutes.
His confidence would also not have been helped by the loss of Henderson just before the half-hour, with the 23-year-old Phillips arriving off the bench as the senior partner despite making just his eighth appearance for the club.
At least Alisson, responsible for three errors in his last two league matches, was back on form with a good save to deny a diving Seamus Coleman header from Lucas Digne’s cross.
Pickford, too, brought his A game as having palmed away an early Sadio Mane cross he flew to his right to tip Henderson’s swerving volley around the post before the Liverpool captain’s exit.
The England number one was in action again catching a Mane header early in the second half, with Mason Holgate also cutting out a dangerous Trent Alexander-Arnold cross and Michael Keane producing a brilliant goal-saving tackle on Mane, who had moved more centrally.
Pickford dived at the feet of Mohamed Salah as Liverpool turned up the pressure without really laying siege to the Everton goal.
Holes began to open up in Liverpool’s defence and from a counter-attack substitute Dominic Calvert-Lewin, deemed not fit enough to start after missing two matches with a hamstring problem, was adjudged to have been brought down inside the box by Alexander-Arnold.
Referee Chris Kavanagh was asked by VAR to look at the pitchside monitor but the official took barely a few seconds to decide he had made the right decision and another substitute Sigurdsson stroked home the penalty to spark wild celebrations.