Liverpool maintained their 100% start with victory over Arsenal while champions Man City returned to winning ways away at Bournemouth.
Frank Lampard picked up his first win as Chelsea boss while top-six rivals Man Utd and Spurs both lost at home.
Leicester and Wolves remain unbeaten while Watford are the only team to have lost all three of their matches so far this season.
Let’s take a look at all the results from the English Premier League 2019/20 Round 3.
Aston Villa 2-0 Everton
Norwich City 2-3 Chelsea
Brighton & Hove Albion 0-2 Southampton
Manchester United 1-2 Crystal Palace
Watford 1-3 West Ham United
Sheffield United 1-2 Leicester City
Liverpool 3-1 Arsenal>
Bournemouth 1-3 Manchester City
Tottenham Hotspur 0-1 Newcastle United
Wolverhampton Wanderers 1-1 Burnley
Aston Villa picked up their first win back in the top-flight with a 2-0 victory over Everton at Villa Park.
New signing Wesley opened the scoring after 21 minutes before substitute Anwar El Ghazi sealed the victory in injury time.
Despite having just 35% possession, Dean Smith’s side held on to claim a vital three points.
Norwich hosted Chelsea in the early kick-off on Saturday and the two teams played out a thriller at Carrow Road.
Tammy Abraham scored twice for Chelsea while fellow youngster Mason Mount also got on the scoresheet.
Teemu Pukki scored his fifth goal in three matches but couldn’t prevent Norwich eventually losing 3-2.
Goals from Moussa Djenepo and Nathan Redmond secured Southampton's first win of the season as Brighton’s Florin Andone was shown a red card after just half an hour.
Crystal Palace claimed a rare win at Old Trafford as Patrick van Aanholt scored a 93rd minute winner.
Marcus Rashford missed a penalty after Jordan Ayew gave Palace the lead. Daniel James thought he had rescued a point for United however the match finished 2-1.
Two goals from Sebastien Haller helped West Ham to a comfortable 3-1 victory at Watford while a brilliant Harvey Barnes strike sealed a 2-1 win for Leicester against Sheff Utd.
Mohamed Salah scored twice as Liverpool beat Arsenal 3-1 in Saturday’s late kick-off.
Joel Matip opened the scoring for the Reds before Lucas Torreira bagged a late consolation for the Gunners.
Sergio Aguero opened and finished the scoring in Man City’s 3-1 win away at Bournemouth.
Raheem Sterling doubled the visitor’s lead before Harry Wilson scored a stunning free-kick in first-half injury time.
Newcastle picked up a hard-fought win at Tottenham as Joelinton scored his first for the club and the only goal of the game.
Raul Jimenez scored a 97th minute penalty to save a point for Wolves after Ashley Barnes gave Burnley the lead in the first-half. The match finished 1-1 after what was an exciting encounter.