Arsenal squandered a narrow one-goal lead with 15 minutes left to play as Wolves held them to a 1-1 draw at the Emirates on Saturday.
Manchester United saw their recent run of results snap as Bournemouth handed them a 1-0 defeat, with Joshua King scoring the only goal of the game.
Jordan Henderson and Mohamed Salah were the heroes in the second half as Liverpool came from behind to beat Tottenham 2-1 at Anfield on Sunday.
Manchester United ended their four-game winless streak in the Premier League, as they defeated Norwich City 3-1 at Carrow Road on Sunday.
Christian Pulisic was the hat-trick hero for Chelsea as they survived a late scare to beat Burnley 4-2 at Turf Moor on Saturday evening.
Liverpool came from behind to salvage a point against arch rivals Manchester United, as their perfect start to the Premier League season came to a halt.
Marcos Alonso made the difference for Chelsea against a resolute Newcastle United side as they grabbed a 1-0 win at Stamford Bridge on Saturday.
Tammy Abraham and Mason Mount continued their splendid start to the season, as Chelsea cruised to a 4-1 win over Southampton on Sunday.
After two games without a win, Real Madrid bounced back strongly, beating Granada 4-2 at the Santiago Bernabeu on Saturday afternoon.
James Milner scored the winner deep into injury time as Liverpool continued their perfect start to the Premier League season with a 2-1 win over Leicester City.