Virgil Van Dijk's 100th-minute header ensured that the Reds had the bragging rights as they won the first Merseyside derby held at Hill Dickinson.
Mohammed Salah fired his side in front minutes after Iliman Ndiaye thought he opened the scoring but was disallowed for offside.
Beto equalised for Everton early in the second-half as he tapped in from close range following a low ball across from Kiernan Dewsbury-Hall.
However in the 10th minute of added time the Blues failed to deal with a corner and Van Dijk headed past the helpless Jordan Pickford as the Reds go eight points clear and have ended Everton's slim hope of Champions League qualification.
Branthwaite worry
It's been a season plagued with injuries for Jarrad Branthwaite as the 23-year-old was stretchered off and was brought to tears as it looks like his season is over.
The defender, has only made ten appearances all season due to a hamstring issue and went down after holding his hamstring.
It's another blow to Everton as Branthwaite showed his importance on numerous occasions against Liverpool.
The England international won four ground duels, and two aerial duels. At times Branthwaite shown how important his recovery pace is as he stopped Alexander Isak going through one-on-one, in the first-half.
On the ball the 23-year-old showed his importance as in the first-half his pass opened up Liverpool and led to Beto wasting a one-on-one at 0-0.
Subs failed to make an impact
The introduction of Tyrique George and Thierno Barry didn't bring the same effect as it did last week against Brentford on April 12.
After Everton's leveller the Blues had all the momentum but failed to test third-choice goalkeeper Freddie Woodman after he replaced Giorgi Mamardashvili due to injury.
Beto, throughout was proving to be a handful as Van Dijk, and Ibrahima Konate were in a constant battle throughout with the 28-year-old.
Barry lost possession five times and Everton lost that threat up-front as they failed to take the initiative to their rivals after levelling.
George was similar as he also couldn't get himself into the game. In cameos the loanee has shown how direct he can be for the Blues but was unable to make an impact.
Liverpool showed the importance of a strong bench as they brought on Alexis Mac Allister, Jeremie Frimpong, Rio Ngumoha and Milos Kerkez.
Set piece concerns
It hasn't been the first time this season that teams target Jordan Pickford on corners. Against Liverpool, Arne Slot's side caused problems from corners including one, where Pickford pushed it out for another corner.
Throughout this season Newcastle United, Tottenham Hotspur and Brentford have all caused problems for David Moyes's side from corners.
Opposition players crowd Pickford so he's unable to get set and once again it was something that Everton failed to deal with.
Salah, Konate, Van Dijk and Mac Allister were near Pickford and all ran off which led to the Dutchman getting to the ball before James Tarkowski and heading past Pickford.
European hopes are still alive
Despite the setback Everton are only one point behind sixth place Chelsea and are still firmly in the mix. The Blues have to travel to West Ham, Crystal Palace and Tottenham, meanwhile they face Manchester City and Sunderland at home.
Given where Everton have been in recent years, and the challenges that follow when moving stadium, the Blues are still in a strong position to get over 50 points which last happened in 2020/21 with Carlo Ancelotti.
The Champions League dream might have faded but with five games to go Everton are still within a shout of some form of European football.