Hal Robson-Kanu fired his first goal of the season as West Brom clinched a 2-1 Premier League win over 10-man Southampton at St Mary's.
Islam Slimani eased any growing relegation pressure at Leicester as the champions held on to beat West Ham 1-0.
Anthony Martial and Paul Pogba struck in the closing minutes to hand Manchester United a deserved three points against Middlesbrough at Old Trafford.
Willian scored twice as Chelsea held off valiant Stoke for a Premier League record 13th successive win in a single season.
Jurgen Klopp won the battle of managerial masterminds at Anfield as Liverpool's 1-0 victory put a dent in Manchester City's title aspirations.
Liverpool warmed up for their mouthwatering clash against top-four rivals Manchester City later this week with a confident 4-1 win over Stoke.
Three goals in the final 18 minutes saw Manchester City climb to second in the Premier League table courtesy of a laboured 3-0 win at Hull.
Kevin Mirallas and Romelu Lukaku struck to sink Leicester and hand Everton their first away win since September.
Henrikh Mkhitaryan's moment of magic capped a comprehensive 3-1 Manchester United win and chastening Old Trafford return for Sunderland manager David Moyes.
Chelsea set a new club record of 12 straight Premier League wins and extended their lead at the top of the table with a 3-0 victory over Bournemouth at Stamford Bridge on Monday.
Olivier Giroud marked his first Premier League start of the season by heading home a late winner as Arsenal eked out a 1-0 victory over a resolute West Brom.
Striker Daniel Sturridge came off the bench to play a pivotal part in Liverpool snatching a winner in the fifth minute of added time of the 227th Merseyside derby.
Manchester City recovered from an early Arsenal goal to produce a dominant second-half display and record a 2-1 win that moves them up to second place in the Premier League table.
Danny Rose broke Burnley hearts with a second-half winner as Tottenham snatched a 2-1 victory and moved to within a point of the Premier League's top four.
Manchester United moved level on points with fifth-placed Tottenham Hotspur, for 24 hours at least, after beating West Bromwich Albion 2-0 at The Hawthorns.
Ten-man Leicester City rallied against the odds to overcome Jamie Vardy's 28th-minute dismissal and a two-goal deficit to draw 2-2 at Stoke City.
Chelsea extended their lead at the top of the Premier League to nine points, for at least a day, with a 1-0 win against Crystal Palace at Selhurst Park as Diego Costa scored his 50th goal for the club.
Zlatan Ibrahimovic struck a late winner as Manchester United secured victory at Crystal Palace after once again threatening to drop points from a winning position.
Jurgen Klopp's decision to drop goalkeeper Loris Karius was vindicated on a night when the brilliance of Adam Lallana swept Liverpool to a 3-0 win over Middlesbrough at the Riverside Stadium.
Christian Eriksen laid on an attacking masterclass by scoring twice and setting up another as Tottenham cruised to a 3-0 victory over struggling Hull.
Pablo Zabaleta's first goal for two years and a late David Silva strike fired Manchester City to a much-needed -- but unconvincing -- 2-0 win over Watford.
Cesc Fabregas' first Premier League goal of the season handed Chelsea victory at Sunderland and sent them six points clear at the top of the table.
Ashley Williams scored a late winner for Everton as they came from behind to win 2-1 and inflict a first Premier League defeat on Arsenal since the opening day of the season.
Marc Pugh capped his first start of the season with a smart strike as Bournemouth outclassed Leicester 1-0 on the south coast.
Liverpool lost ground on leaders Chelsea as they were held to a 2-2 draw by struggling West Ham United at Anfield.
Manchester United closed the gap on fifth place to three points thanks to a scrappy 1-0 win against Tottenham Hotspur at Old Trafford on Sunday.
Diego Costa's fifth goal in six games broke West Brom's stubborn resistance and sealed Chelsea's ninth consecutive Premier League victory.
Jamie Vardy scored a hat trick as Leicester City put their recent poor form behind them with a 4-2 win over Manchester City at the King Power Stadium.
Arsenal came from behind to go top of the Premier League table and extend their unbeaten league run to 14 league games with a 3-1 win over Stoke at the Emirates Stadium.
Marouane Fellaini gave away a late penalty as his old club Everton snatched a 1-1 draw with Manchester United to leave Jose Mourinho frustrated again.
West Ham United beat Everton 3-1 at Goodison Park on Sunday to secure their first Premier League points of the season as Marco Silva tasted defeat for the first time as Everton manager.
Manchester United ruined Watford's first perfect start to a Premier League season with a 2-1 victory at Vicarage Road on Saturday.
Manchester City comfortably defeated Fulham 3-0 at the Etihad Stadium on Saturday to stay within two points of leaders Liverpool and Chelsea.
A free kick by midfielder Granit Xhaka and a goal by Mesut Ozil gave Arsenal a 2-1 win at Newcastle United despite a stuttering first-half performance on Saturday.
A hat trick from Eden Hazard gave Chelsea their fifth win in five games, a 4-1 victory over Cardiff City that sent them to the top of the Premier League on Saturday.
Liverpool continued their perfect start to the season after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley Stadium on Saturday.
Watford came from behind with two set-piece goals to beat Tottenham Hotspur 2-1 at Vicarage Road on Sunday, ending the visitors' perfect start to the Premier League season while maintaining their own.
Manchester United fans showed their backing for manager Jose Mourinho after Romelu Lukaku struck twice as United returned to winning ways after two successive Premier League losses with a 2-0 victory at Burnley on Sunday.
Alexandre Lacazette scored his first goal of the season in his first start under Unai Emery, handing Arsenal a 3-2 victory away against Cardiff City.
Raheem Sterling and Kyle Walker each scored as Manchester City defeated Newcastle United 2-1 at the Etihad Stadium on Saturday.
Chelsea stretched their perfect Premier League start to four games after second-half goals from substitute Pedro and Eden Hazard gave them a 2-0 home win over Bournemouth on Saturday.
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 on Saturday at the King Power Stadium.
Liverpool will host Chelsea while Frank Lampard's Derby County will visit Manchester United following the third-round draw for the Carabao Cup held on Thursday.
Tottenham piled on more woe for Manchester United, running out 3-0 winners at Old Trafford on Monday night to hand the hosts a second Premier League defeat in as many weeks.
Chelsea left it late but came away with a 2-1 win over Newcastle thanks to a late DeAndre Yedlin own goal St James' Park on Sunday.
Unfancied Watford continued their great start to the Premier League season with a third successive win when they beat visiting Crystal Palace 2-1 on Sunday.
Mohamed Salah's 23rd-minute strike was enough to earn Liverpool a 1-0 win over a dogged Brighton and Hove Albion and give them an early top spot in the Premier League with three wins out of three.
Arsenal celebrated their first Premier League win of the season under new manager Unai Emery after coming from behind to beat London rivals West Ham United 3-1 in an action-packed match on Saturday.
Manchester City stumbled to a 1-1 draw at Wolves in a tense lunchtime encounter at Molineux.
Liverpool's James Milner's converted a penalty on the stroke of halftime and Sadio Mane added a late second goal to secure a hard-fought 2-0 win at Crystal Palace in the Premier League on Monday.
Manchester United conceded three first-half goals as they slumped to a 3-2 defeat at Brighton in a game illuminated by a superb goal from Seagulls striker Glenn Murray.
Sergio Aguero scored his 13th hat trick for Manchester City as the Premier League champions brushed Huddersfield aside in a 6-1 win at the Etihad Stadium.
Chelsea secured their second straight win of the season and sentenced Arsenal to a second defeat with a 3-2 win in a Stamford Bridge thriller that had seen Arsenal fight back from two goals down to level.
Leicester City had Jamie Vardy sent off but it did not stop them from recording a comfortable 2-0 home victory over Wolverhampton Wanderers in the Premier League on Saturday.
Harry Kane finally ended his August goalscoring drought as England's World Cup luminaries inspired Tottenham Hotspur to a morale-boosting 3-1 Premier League win over newcomers Fulham on Saturday.
Kenedy missed a 96th-minute penalty as Cardiff secured a 0-0 draw against 10-man Newcastle in their first home game back in the Premier League.
Manchester City midfielder Kevin De Bruyne is facing a spell on the sidelines after injuring his right knee in training on Wednesday.
Manchester City, who romped to Premier League success by 19 points last season, began the defence of their title with a 2-0 win away against Arsenal and new manager Unai Emery on Sunday.
Sadio Mane had two goals for the first time since February 2017 and Mohamed Salah also scored as Liverpool opened their Premier League season with a 4-0 victory over West Ham United at Anfield.
Richarlison scored twice in his first Premier League appearance for 10-man Everton, but a late goal from Raul Jimenez helped Wolverhampton Wanderers salvage a 2-2 draw at the Molineux Stadium.