Chelsea celebrated lifting the Premier League trophy with a record 30th win as relegated Sunderland were dispatched with ease at Stamford Bridge.
Alexis Sanchez helped 10-man Arsenal to a 3-1 win over Everton but Arsene Wenger's side missed out on Champions League qualification.
Ruthless Harry Kane struck four goals as Tottenham dismantled Leicester 6-1.
Southampton struggled to relieve the pressure building on manager Claude Puel after an under-strength Manchester United held them to a 0-0 home draw.
Manchester City moved up to third in the Premier League with a comfortable 3-1 win over West Brom on an emotional night at the Etihad Stadium.
Alexis Sanchez hit a brace as Arsenal secured victory over relegated Sunderland in front of a sparsely populated Emirates Stadium to keep alive their dwindling hopes of Champions League qualification.
Cesc Fabregas scored in the 88th minute to lift champions Chelsea to a wild 4-3 win over Watford on Monday night to match the Premier League record for wins in a season.
Tottenham bid a victorious farewell to White Hart Lane after 118 years as Mauricio Pochettino's side outmanoeuvred Manchester United.
Philippe Coutinho kept Liverpool's Champions League challenge in their own hands by destroying West Ham at the London Stadium.
Riyad Mahrez's penalty slip ensured Manchester City did not take a tumble of their own in the Champions League race, moving third with a 2-1 win over Leicester at the Etihad Stadium.
Chelsea secured the Premier League title for the second time in three seasons when substitute Michy Batshuayi scored late to supply a 1-0 win at West Brom on Friday night.
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.
Manchester City's quadruple trophy bid was sensationally derailed by a shocking 1-0 defeat at third-division Wigan in the FA Cup fifth round on Monday.
Substitute Steve Davies earned Rochdale an FA Cup fifth-round replay at Wembley Stadium with his remarkable stoppage-time equaliser against Tottenham Hotspur at Spotland.
Manchester United overcame the video assistant referee's controversial intervention and reached the FA Cup quarterfinals thanks to Romelu Lukaku's brace at Huddersfield.
Willian dispatched two inch-perfect finishes as Chelsea cruised past Hull 4-0 and into the FA Cup quarter-finals.
Sheffield Wednesday fan Jamie Vardy put the Blades to the sword as Leicester knocked Sheffield United out of the FA Cup.
Chelsea eased the growing pressure on Antonio Conte and returned to the Premier League's top four with a convincing 3-0 win over West Brom.
Liverpool moved back above Tottenham and into third place in the Premier League table as two first-half goals gave them a routine 2-0 victory at struggling Southampton.
Matt Ritchie scored a second-half winner for Newcastle as they lifted themselves out of the relegation places with a 1-0 victory over Manchester United at St James' Park.
Sergio Aguero scored four times as Manchester City extended their Premier League lead to 16 points with a 5-1 demolition of Leicester at the Etihad Stadium.
Everton's Sam Allardyce won the battle of ex-England managers at Goodison Park to ease growing pressure with a 3-1 victory over Roy Hodgson's struggling Crystal Palace.
Harry Kane proved Arsenal's nemesis again as his bullet header earned Tottenham a deserved 1-0 victory in the North London derby.
Erik Lamela scored his first goal in 17 months as Tottenham sauntered past Newport and into the fifth round of the FA Cup.
Swansea recorded their biggest-ever FA Cup win as Notts County were demolished 8-1 at the Liberty Stadium.
Antonio Conte's future as Chelsea boss was cast into further doubt as his 10 men were thrashed 4-1 by Watford on Monday night.
Mohamed Salah and Harry Kane traded stoppage-time goals as Liverpool and Tottenham drew 2-2 in a wild affair at Anfield on Sunday.
Newcastle resisted intense pressure from Crystal Palace to earn a 1-1 draw at Selhurst Park that again took them clear of the bottom three.
`Aaron Ramsey hit a hat trick with Arsenal fans treated to their first showing of their January transfers in tandem as both Henrikh Mkhitaryan and Pierre-Emerick Aubameyang shone in a comfortable 5-1 win over Everton.
Alexis Sanchez's first goal for Manchester United wrapped up a 2-0 victory against Huddersfield on a day when the clubs came together to remember those who lost their lives in the Munich air disaster.
Swansea's resurgence continued as they climbed out of the Premier League relegation zone with a 1-1 draw at Leicester, who were again without want-away midfielder Riyad Mahrez.
Johann Berg Gudmundsson struck a late equaliser as Burnley grabbed a 1-1 draw against Premier League leaders Manchester City at Turf Moor.
Christian Eriksen scored within 11 seconds as Tottenham brushed aside a below-par Manchester United to seal a crunch 2-0 victory in the race for the top four.
Kevin De Bruyne was again the inspiration as Manchester City opened up a 15-point lead at the top of the Premier League with a 3-0 win over West Brom.
Theo Walcott's maiden Everton goals secured a first win in eight matches as a 2-1 triumph over Leicester arrested their slide under Sam Allardyce.
Bournemouth scored three goals in 16 remarkable second-half minutes to record a sensational 3-0 victory against Chelsea at Stamford Bridge on Wednesday evening.
Arsenal have completed the signing of striker Pierre-Emerick Aubameyang from Borussia Dortmund for a fee of €63.75 million (£56m).
Chelsea have completed the signing of Olivier Giroud from Arsenal for a reported £16.25 million on an 18-month contract.
Tottenham Hotspur have completed the signing of winger Lucas Moura from Paris Saint-Germain for a fee of в‚¬28 million.
Liverpool bounced back to winning ways in the Premier League and maintained their Champions League challenge with a 3-0 win at Huddersfield.
Swansea climbed out of the relegation zone for the first time in three months as Petr Cech's dreadful howler helped condemn Arsenal to a 3-1 defeat at the Liberty Stadium.
Two first-half goals were enough to see Manchester City comfortably through to the FA Cup fifth round at Championship side Cardiff City.