Frank Lampard's Everton must mount a dramatic revival in the final month of this campaign to ensure that the 241st edition of this 128-year-old fixture will take place in the Premier League next season.
But this game was what a football rivalry boils down to when one team is up and the other is down. Liverpool could win everything there is to win this season, but Everton are now desperately battling to avoid being relegated from the top division for the first time since 1951. They are poles apart, and Liverpool's goals from Andy Robertson and Divock Origi could have big implications for both sides over the weeks ahead.
"Everton did what they had to do, but we deserved the three points," Liverpool manager Jurgen Klopp said. "If anybody thinks we fly through these games, I can apologise: It won't happen."
"If we can create atmospheres like today, it's difficult to deal with us for 95 minutes, but thank God the game has two halves because we didn't play particularly well in the first half."
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Enduring Liverpool's success has been tough enough for Evertonians in recent years, but imagine how it will feel this time around if the Reds bag all four trophies and the Blues end up relegated to the EFL Championship, with this defeat at Anfield leaving Everton in the bottom three for the first time since December 2019.
And add in the fact that the two sets of supporters really don't like each other -- some of the chants aired at Anfield highlighted the animosity that has grown since the days when it was dubbed the "Friendly Derby" in the 1980s -- and it was definitely a case of fear and loathing on Merseyside.
The fear was felt on both sides, with the dread of their neighbours inflicting a damaging blow to a season's objectives, while the loathing was there with the Everton fans turning their backs when "You'll Never Walk Alone" was sung by the home fans, along with songs relating to the 1985 Heysel Stadium disaster, when 39 Juventus fans were killed in rioting prior to the European Cup final against Liverpool in Brussels.
In response, the Liverpool fans taunted their city neighbours with chants of "This is your last trip to Anfield!" and "Going Down" as Klopp's players claimed the victory that once again moved them to within a point of leaders Manchester City in the race for the title.
City and Liverpool both have five games left, and neither look like dropping points between now and the final round of fixtures on May 22. For Liverpool, who have already won the Carabao Cup this season, there is also the pursuit of glory in the Champions League, where they face Villarreal in the semifinals, and an FA Cup clash with Chelsea on May 15.
Yet this was a game that neither side would have relished because the motivation of the opponent was at a higher level than a routine fixture. That usually leads to greater unpredictability and emotion, and top teams tend to succeed because they take the unpredictability and emotion out of the equation.
Upsetting a big team's rhythm is often the only tactic available to an unfancied side, and that was Everton's approach here. Lampard's players were tough, belligerent and ready to fight, breaking the game down with time-wasting and tactical fouls.
They attempted to drag Liverpool into a scrap, and it worked in the first half, with referee Stuart Attwell unable to control the two teams. In Anthony Gordon, Everton had a young, spirited winger who gave Liverpool problems with his pace and direct running. The 21-year-old, booked for diving in the penalty area in the first half, was unfortunate not to win a penalty when he appeared to be shoved to the ground by Joel Matip eight minutes into the second half.
"I think they both could have been penalties," Lampard said. "But you often don't get them at Anfield. The fact there's contact and he gets booked is crazy. The second one was a foul [anywhere else] on the pitch. Sometimes you don't get them here."
As so often happens, though, the top teams find a way to win when the opponent is dogged and stubborn, and Liverpool did find a way, with Klopp's 60th-minute substitutions ultimately proving decisive.
Origi and Luis Diaz replaced Naby Keita and Sadio Mane, and within two minutes, Origi had created the opening for Mohamed Salah to cross for Robertson, who headed in his first goal at Anfield since September 2020.
Origi has earned himself a place in Liverpool folklore with his match-winning contributions as a substitute, and the Belgium forward did it again when he made it 2-0, heading in from close range after Diaz had attempted an overhead kick. That made it six goals in 12 games against Everton -- twice as many as he has scored against any other team.
It was a goal that secured victory and banished Liverpool's nerves, putting them another win closer to unprecedented success.
But for Everton, there was no positive or silver lining. They face Chelsea at home next and must also travel to top-four-chasing Arsenal. With relegation rivals Burnley facing second-bottom Watford on Saturday, there is a real prospect of Everton being in even deeper trouble by the time they kick off against Chelsea on Sunday.
They have six games to save their season and avoid relegation. That is in Everton's hands. They can only close their eyes and hope for the best when it comes to Liverpool and their pursuit of history.