Tottenham beat Chelsea in the late kickoff with a 3-1 win at Wembley.
Dele Alli put the hosts ahead with a header from Christian Eriksen's free kick, before Harry Kane doubled their lead with a strike from distance.
Heung-Min Son scored a sunning solo goal to put Spurs three up after the break.
Olivier Giroud grabbed a consolation for Chelsea late on, but Maurizio Sarri's unbeaten start as Blues boss comes to an end.
Manchester City maintained their unbeaten league start to the season after thrashing West Ham 4-0 at London Stadium.
David Silva has scored more goals against West Ham than any other side, and added another to his tally after 11 minutes at London Stadium.
Manuel Pellegrini's plan to attack City was failing, and Raheem Sterling doubled the lead soon after their opener, tapping in a low cross from Leroy Sane.
The champions were in a ruthless mood, and soon made it three after Sane grabbed a goal of his own, with Sterling returning the favour with an assist.
Sane got his second of the game in second half stoppage time to make it four as City won in emphatic fashion.
Liverpool ensured they kept pace with City with a 3-0 win at Watford.
Gerard Deulofeu thought he had given the hosts the lead after just two minutes, but his well-taken effort was ruled out for offside.
A scrappy encounter bereft of chances had to wait until the second half for any action, with Sadio Mane hitting the post and Will Hughes being denied a penalty within 10 minutes of the restart.
Liverpool finally took the lead after 67 minutes through Mohamed Salah, whose driven effort gave Ben Foster no chance.
Trent Alexander-Arnold doubled Liverpool's lead with a free kick from 30 yards to put Liverpool two to the good.
Jordan Henderson was sent off for a second bookable offence late on, but Roberto Firmino was able to score soon after as Liverpool held on to maintain their own unbeaten league start to the season.
Manchester United's frustrations rumbled on at Old Trafford with a 0-0 draw with Crystal Palace.
Patrick van Aanholt should have opened the scoring in the first half for Palace with a low drive, before Chris Smalling should have done so at the other end minutes later but his header went wide.
Palace had the ball in the net after Victor Lindelof put the ball in his own net, but Cheikhou Kouyate was judged to have been offside.
United had a goal ruled out for offside themselves at the start of the second half with Romelu Lukaku being denied his first goal in 11 club games.
The draw sees United climb to seventh place, though a win would have seen them climb to sixth, while Palace move a point clear of the relegation zone.
Claudio Ranieri had a dream start as Fulham manager as they saw off relegation rivals Southampton 3-2 at Craven Cottage.
Stuart Armstrong grabbed his first Southampton goal after Fulham failed to clear their lines, and the Scotland international was on hand to slot it past Sergio Rico.
They were not ahead for long though, as Aleksandar Mitrovic headed in an equaliser from Maxime Le Marchand's cross.
Fulham managed to turn the game on its head just before the break, as Ryan Sessegnon dribbled his way down the left wing and found Andre Schurrle with a cross, who finished at the far post.
Lighting struck twice for Armstrong as he bagged his second Southampton goal after 53 minutes, finding the top corner with a fine effort, before Mitrovic grabbed a brace of his own with a volley at the far post.
Fulham climb off the foot of the table and are only in the drop zone on goal difference, while Southampton are just out of it because of their own goal difference.
Ten-man Leicester came from behind to salvage a 1-1 draw at Brighton.
Glenn Murray's first goal against Leicester came after 15 minutes, heading the ball on at the near post and beating Kasper Schmeichel.
The first half went from bad to worse for the away side as James Maddison received a second yellow card after diving.
With 10 minutes to go, Kelechi Iheanacho was brought down by Beram Kayal in the box, and Jamie Vardy converted from the spot to grab a point for Leicester.
Everton's good start to the season continued with a hard fought 1-0 win over Cardiff.
Gylfi Sigurdsson's effort from six yards was all that separated the sides in a tight game at Goodison Park.
Cardiff remain in the relegation zone after suffering their ninth league defeat of the season, while Everton climb into sixth.