Sadio Mane and Roberto Firmino scored in the first half as Liverpool won their first four Premier League games for the first time with a 2-1 victory over Leicester City at the King Power Stadium.
Mane scored in the 10th minute and Firmino scored in the 45th, but a 63rd-minute gaffe by Liverpool goalkeeper Alisson cost him a fourth consecutive Premier League clean sheet when Rachid Ghezzal slotted home.
Pedro and Eden Hazard preserved Chelsea's perfect start to the season as they claimed a 2-0 victory against Bournemouth at Stamford Bridge.
Having replaced Willian in the 67th minute, Pedro ran onto a through ball from Olivier Giroud, then tucked his right-footed shot from 18 yards just inside the left post to beat Asmir Begovic.
Hazard then doubled the lead in the 85th minute for his second league goal of the season, as Chelsea won their first four games to start the season for the first time since they won the Premier League in 2014-15.
Raheem Sterling and Kyle Walker each scored as Manchester City defeated Newcastle United 2-1 at the Etihad Stadium on Saturday.
Sterling opened the scoring in the seventh minute with his second goal of the season after he finished from 16 yards out after curling a right-footed shot past goalkeeper Martin Dubravka.
After United States international DeAndre Yedlin scored his first Premier League goal in the 30th minute, Walker broke the deadlock in the 52nd by rifling a shot from 25 yards out.
Glenn Murray scored two goals, including a penalty in the 84th minute, as Brighton & Hove Albion recovered from a two-goal deficit to draw 2-2 against Fulham at the AmEx Stadium.
Andre Schurrle scored from a through ball by Jean Michel Seri in the 43rd minute before Aleksandar Mitrovic scored his fourth goal in his last three games in the 63rd.
And while Brighton's Pascal Gross had a penalty saved in the 25th minute by Marcus Bettinelli after Glenn Murray was brought down in the area, Murray pulled one back for Brighton in the 67th minute and then equalised after a penalty was awarded for a handball on Mitrovic.
Danny Ings scored his 50th Premier League goal as Southampton beat Crystal Palace 2-0 at Selhurst Park.
Ings, on loan from Liverpool, scored his second goal of the season in the 47th minute, running onto a pass from Cedric Soares at midfield before slotting home between Wayne Hennessey's legs.
Charlie Austin failed to increase Southampton's lead when his 65th-minute penalty was saved by Hennessey, but Pierre-Emile Hojbjerg scored in the 92nd minute to put it away.
Palace were without Wilfried Zaha, who was not included in the matchday squad after injuring a groin muscle in training.
Dominic Calvert-Lewin equalised just two minutes after Philip Billing scored as Everton drew 1-1 against Huddersfield Town at Goodison Park.
Billing scored from a header off a corner in the 34th minute for his first Premier League goal, but Calvert-Lewin, who scored two goals in the Carabao Cup victory against Rotherham United on Wednesday, answered from a cross by Lucas Digne.
Everton have not lost to Huddersfield at home since Sept. 25, 1937.
Wolverhampton Wanderers defeated West Ham United 1-0 at the London Stadium after new signing Adama Traore scored in the 93rd minute.
West Ham have now lost four consecutive games for the first time since 2010.