Liverpool swept aside Nottingham Forest 3-0 on Sunday as Aston Villa joined them in the Premier League top four ahead of the Manchester derby at Old Trafford.
Diogo Jota, Darwin Nunez and Mohamed Salah were on target for Jurgen Klopp's men, who were without Luis Diaz after his parents were kidnapped in Colombia.
Jota gave Liverpool a 31st-minute lead, turning home a rebound after Matt Turner had made a save.
In celebration, he ran to manager Jurgen Klopp, who handed him a miniature Diaz number seven shirt to hold aloft.
Nunez doubled Liverpool's lead four minutes later with an emphatic near-post finish after Dominik Szoboszlai's cut-back.
Mohamed Salah struck Liverpool's third goal in the 77th minute, profiting from Turner's error to slide the ball into an empty net.
Diaz was left out of the matchday squad at Anfield.
Colombia President Gustavo Petro said on Saturday that the winger's mother had been rescued from kidnappers but the search remained ongoing for his father.
Klopp said before the match that it was a "worrying situation for all of us".
"We had to obviously make a late change because of the private situation involving Luis Diaz," he added.
"It was a pretty tough night. I have never had that before. It's a new experience I never needed."
- Villa run -
High-flying Aston Villa won their 12th consecutive home game in the Premier League, beating struggling Luton 3-1.
John McGinn coolly finished from a good set-piece routine in the 17th minute and the home side doubled their lead four minutes after the restart when Moussa Diaby drilled home a loose ball.
Villa made it 3-0 just after the hour when Tom Lockyer turned Diaby's cross into his own net. A late own goal from goalkeeper Emiliano Martinez made it 3-1.
The win lifts Unai Emery's men into fourth place in the table ahead of the Manchester derby at Old Trafford.
Champions City will return to the top four if they beat United at Old Trafford, where the packed ground celebrated the life of the late Bobby Charlton before kick-off.
Brighton lost further ground after their sparkling start to the season.
The south coast club took a 1-0 lead through Evan Ferguson, who picked up the ball outside the box and expertly finished passed Bernd Leno with his left foot.
Fulham levelled 20 minutes after the restart through midfielder Joao Palhinha, who found the top corner from the edge of the box.
Earlier, Dominic Calvert-Lewin scored the only goal of the game as Everton beat West Ham 1-0 to give themselves breathing space above the Premier League relegation zone.
The England forward found the net early in the second half with an arrowing low shot from the edge of the area and the home side were unable to respond.
The win lifts Everton five points clear of the bottom three while it was West Ham's fourth defeat in six league games.
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