Mohamed Salah made a great start for Liverpool in front of the home crowd at Anfield when he scored 1–0 on a penalty in the 29th minute.
Curtis Jones secured the win with a 2–1 score against Chelsea, even though there was still a lot of play left after the goal in the 51st minute.
The win puts the club at the top of the Premier League table after eight rounds with 21 points.
One point behind is Manchester City – which decided the game late in the 2–1 win over Wolverhampton.
As early as the seventh minute, City got a setback in the away game when Norwegian Jørgen Strand Larsen got the ball from Nélson Semedo and scored the 1–0 goal for the home team.
After just over half an hour, Joško Gvardiol equalized, and it wasn't until the fifth minute of added time that the winning goal came.
John Stones – who in the 98th minute scored the equalizer in the thrilling match against Arsenal earlier in the season – reached the highest on Phil Foden's corner and headed in the winning goal.
But the guests had to wait to celebrate.
The goal was reviewed by VAR for offside, as Bernardo Silva was on the wrong side of the line. Referee Chris Kavanagh listened to the VAR officials in his headphones and then had to run to the side of the pitch to check the situation himself.
There, he made the decision: goal.
Liverpool's and City's wins mean that the clubs have pulled away at the top. Arsenal, which lost to Bournemouth on Saturday, is third on 17 points.