Alexis Sanchez hit his 20th Premier League goal of the season as Arsenal saw off Southampton to keep their Premier League top-four hopes alive.
Chelsea moved within three points of the Premier League title and consigned Middlesbrough to relegation with a dominant 3-0 victory at Stamford Bridge.
Arsenal kept their slim hopes of a top-four finish alive with a comfortable 2-0 win over a much-changed Manchester United side at the Emirates Stadium on Sunday in a first league win for Arsene Wenger over Jose Mourinho.
James Milner had a penalty saved as Liverpool saw their hopes of establishing a cushion in the chase for the top four frustrated by a 0-0 home draw against Southampton.
Swansea moved out of the Premier League relegation zone as Fernando Llorente's first-half header gave them a precious 1-0 victory over Everton.
Manchester City strengthened their hopes of a top-four Premier League finish and moved up to third in the table thanks to a 5-0 victory over Crystal Palace at the Etihad Stadium on Saturday.
Tottenham's title hopes were dealt a decisive blow as Manuel Lanzini's strike gave West Ham a memorable 1-0 win over their London rivals.
Liverpool took a significant step to sealing Champions League qualification as Emre Can scored a goal-of-the-season contender to down Watford on Monday night.
Tottenham Hotspur again ensured Chelsea's lead at the top of the Premier League remains at four points and guaranteed that they will finish above Arsenal as they won White Hart Lane's last-ever North London derby 2-0.
Gabriel Jesus marked his return to Manchester City's starting lineup by grabbing a dramatic late equaliser for his side in a 2-2 draw against relegation-haunted Middlesbrough at the Riverside Stadium.
Chelsea scored three second-half goals to win at Everton and re-establish a seven-point lead over Tottenham Hotspur, who take on their North London rivals Arsenal later on Sunday.
A late equaliser by Gylfi Sigurdsson denied Manchester United the chance to move up into third place and boosted Swansea's chances of escaping the drop in a 1-1 draw at Old Trafford.
Jamie Vardy continued his red-hot run in front of goal as Leicester eased their Premier League relegation fears with a 1-0 win at West Brom.
Marouane Fellaini was sent off as Manchester City and Manchester United settled for a share of the spoils in the Manchester derby, with the two neighbours playing out a goalless draw at the Etihad Stadium.
Christian Eriksen kept Tottenham's title hopes alive with a crucial strike to sink Crystal Palace 1-0.
Arsenal kept their hopes of a top-four Premier League finish alive as a late Robert Huth own goal was enough for them to see off reigning champions Leicester.
Diego Costa ended his lean streak with a double as Premier League leaders Chelsea beat Southampton 4-2 to restore their seven-point advantage over Tottenham.
Crystal Palace took a giant step towards Premier League safety and inflicted a setback on Liverpool's top four hopes as Christian Benteke struck twice on his return to Anfield.
Manchester United cruised to a routine victory at Burnley to move to within a point of fourth-placed Manchester City.
Alexis Sanchez struck an extra-time winner as Arsenal came from behind to beat Manchester City 2-1 in their FA Cup semifinal at Wembley.
Eden Hazard came off the bench to help inspire Chelsea to a 4-2 victory over Tottenham and send them into the FA Cup final, condemning Mauricio Pochettino's men to yet more Wembley woe and giving them a bloody nose ahead of the title run-in.
Mesut Ozil kept alive Arsenal's hopes of a top-four finish as Middlesbrough slid closer to the Premier League exit door on Monday night.
Manchester United threw the Premier League title race open and boosted their hopes of a top-four finish as Jose Mourinho masterminded a 2-0 Old Trafford victory over his former club Chelsea.
Roberto Firmino scored Liverpool's winner as they saw off West Bromwich Albion with a 1-0 victory to move up to third in the Premier League.
Crystal Palace recovered from two goals down to secure a 2-2 draw with Leicester and take their latest step towards preserving their Premier League status.
Manchester City moved into third place in the Premier League as Vincent Kompany scored to spark a 3-0 win at Southampton.
Tottenham Hotspur made it seven home league wins in a row and cut the gap on leaders Chelsea to four points ahead of Sunday's games with a dominant display as they won 4-0 against Bournemouth.
Crystal Palace dominated Arsenal 3-0 on Monday night to increase the pressure on Arsene Wenger while boosting their own Premier League survival hopes.
Romelu Lukaku's good form in front of goal at Goodison Park continued with a double as Everton's 4-2 victory over Leicester ended Foxes boss Craig Shakespeare's six-game winning run.
Zlatan Ibrahimovic scored his 17th Premier League goal of the season to set Manchester United on course for a 3-0 victory over 10-man Sunderland which moves them up to fifth in the table.
Riyad Mahrez smashed a late penalty over the bar as Manchester City and Liverpool played out a dull 0-0 draw at Anfield.
Ross Barkley scored his first goal for Chelsea to help defeat Southampton 3-0 at St. Mary's on Sunday.
Arsenal midfielder Aaron Ramsey scored the goal of the game as Unai Emery's men made it nine consecutive wins in all competitions with this 5-1 victory over Fulham.
A 90th-minute goal by Alexis Sanchez helped Manchester United complete an unlikely comeback and claim a 3-2 win over Newcastle at Old Trafford on Saturday.
Eric Dier scored his first Premier League goal since April 2017 as Tottenham Hotspur defeated Cardiff City 1-0 at Wembley Stadium on Saturday.
Liverpool's unbeaten start to the Premier League season continued after Daniel Sturridge rescued a point in the dying minutes against Chelsea.
A late own goal from Watford's Craig Cathcart and a Mesut Ozil strike two minutes later gave Arsenal a 2-0 win at the Emirates on Saturday that sent them above the Hornets in the Premier League table.
Harry Kane scored twice as Tottenham Hotspur moved into fourth place in the Premier League with a 2-0 win at bottom club Huddersfield Town on Saturday.
A stunning Sergio Aguero goal capped Manchester City's 2-0 win over Brighton & Hove Albion as Pep Guardiola's champions served further notice that they will again be the side to beat in the Premier League this season.
Manchester United's miserable start to the season continued as they laboured to a 3-1 defeat at West Ham.
The brilliance of Chelsea's Eden Hazard ended Liverpool's 100 percent start to the season as Maurizio Sarri's side enjoyed a 2-1 win at Anfield in the League Cup third round on Wednesday.
Manchester City were made to work but found a way past Oxford United in a 3-0 Carabao Cup victory on Tuesday night.
Manchester United crashed out of the Carabao Cup with a defeat on penalties to Championship side Derby County on Tuesday after the third-round tie ended 2-2 in normal time at Old Trafford.
Two goals in three second-half minutes gave Arsenal a 2-0 victory over Everton at the Emirates Stadium and took them up to sixth in the Premier League table.
Chelsea were denied their sixth successive Premier League win as London rivals West Ham held them to a 0-0 draw at the London Stadium.
Tottenham Hotspur brought an end to a run of three successive defeats as they won 2-1 at Brighton on a damp Saturday evening on the south coast.
A disappointing Manchester United were held to a 1-1 draw at home to promoted Wolverhampton Wanderers at Old Trafford on Saturday, leaving them eight points adrift of Premier League leaders Liverpool.
Sergio Aguero marked his 300th appearance for Manchester City with a familiar landmark goal to set the resurgent Premier League champions on their way to a magnificent 5-0 win at Cardiff City on Saturday.
Liverpool forward Mohamed Salah netted his first league goal since Aug. 25 as the Reds thrashed Southampton 3-0 to make it six Premier League wins out of six and leapfrog Chelsea at the top of the table on Saturday.
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.