Liverpool's haul of 60 points from 23 matches tops the Reds' previous best tally of 59.
Liverpool are top of the Premier League with 60 points while Manchester United are fifth with 44 points.
Trent Alexander-Arnold has emerged as one of Liverpool's brightest young stars as Jurgen Klopp's side chase the club's first English title since 1990.
Liverpool boss Jurgen Klopp does not want this season's potential title triumph to be a one-off.
Saturday's early kick-off saw teenage midfielder Declan Rice score his first West Ham goal in a 1-0 win at home to London rivals Arsenal.
The 26-year-old footballer Mohamed Salah from Egypt finished first with club-mate Senegalese Sadio Mane.
Without Mohamed Salah, Roberto Firmino and Sadio Mane, Liverpool were struggling to get any momentum going forward.
Mohamed Salah scored 44 goals in all competitions for Liverpool last season and has netted 13 times in the 2018/2019 campaign.
Naby Keita has made 18 appearances so far this season but he has failed to feature in the past three matches for Liverpool.
Manchester City recently suffered back-to-back defeats against Crystal Palace and Leicester City.
Manchester City now trail Liverpool by 10 points.
In the other clashes, Manchester United beat Huddersfield 3-1 and Tottenham thrash Bournemouth 5-0.
Mohamed Salah's 11th goal of the season was a classy one and helped subdue a dangerous Wolves side who had made a lively start.
Jose Mourinho said he accepted responsibility for a 5th defeat of the season that leaves Manchester United 11 points adrift of even a top-four finish.
Manchester United manager Jose Mourinho claimed ahead of the game that the league leaders have had luck.
The win over Everton, moved Manchester City two points ahead of Liverpool, who host Manchester United on Sunday.
Manchester United have an impressive recent record against Liverpool, unbeaten in eight league games.
Virgil Van Dijk believes Liverpool can use their Champions League escape against Napoli as a springboard to win Europe's elite club competition.