Nemanja Matic struck in stoppage time as Manchester United came from two goals down to secure a vital 3-2 victory at Crystal Palace.
Bernardo Silva scored the only goal as Manchester City took another stride towards the Premier League title with a 1-0 victory over Chelsea.
Arsene Wenger remains under intense pressure as Arsenal were deservedly beaten 2-1 by Brighton & Hove Albion at the Amex Stadium on Sunday.
Tottenham warmed up for their Champions League tie with Juventus by easing to a 2-0 victory over Huddersfield at Wembley.
Mohamed Salah scored for the seventh successive match to continue a remarkable scoring spree that is the best in Europe as Liverpool comfortably beat Newcastle United 2-0.
Manchester City inflicted more pain on Arsene Wenger with a second crushing 3-0 victory over his Arsenal side in the space of four days.
Tottenham overcame Rochdale 6-1 in the FA Cup but video technology reduced the fifth-round replay at Wembley to a farce.
Swansea reached their first FA Cup quarterfinal since 1964 with a 2-0 home victory over Sheffield Wednesday.
Manchester City breezed past woeful Arsenal 3-0 to lift the Carabo Cup, Pep Guardiola's first trophy in English football, at Wembley.
Tottenham Hotspur grabbed an 89th-minute winner against Crystal Palace to move into fourth place after a determined home side had seemed set for a battling draw at Selhurst Park.
Substitute Jesse Lingard headed the winner as Manchester United came from a goal down to beat Chelsea 2-1 at Old Trafford and move back into second place in the Premier League.
Watford moved up to 10th in the table as Troy Deeney's late goal gave them a valuable 1-0 victory over Everton at Vicarage Road.
Liverpool took their goal tally for the season to 103 as they claimed second place in the Premier League with a comfortable 4-1 win over West Ham.
Stoke remain in the relegation zone after an error from goalkeeper Jack Butland meant they had to settle for a 1-1 draw at Leicester.
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.
Arsenal have hired former Paris Saint-Germain manager Unai Emery to take them into a new era following Arsene Wenger's departure, with sources telling that he has signed a three-year contract.
Eden Hazard fired Chelsea to FA Cup glory against Manchester United as Antonio Conte's expected farewell ended with a memorable triumph against old foe Jose Mourinho.
Michael Carrick bade farewell to Old Trafford by helping set up the goal that delivered a 1-0 win for Manchester United over Watford.
Champions Manchester City became the first club to amass 100 Premier League points after Gabriel Jesus scored a dramatic stoppage-time winner at Southampton.
Tottenham said goodbye to Wembley in style as they came from behind to beat Leicester 5-4 in a thrilling final-day Premier League encounter.
Ayoze Perez struck twice to end Chelsea's faint hopes of Champions League qualification as Newcastle secured a top-10 finish on their return to the Premier League.
Liverpool secured a top-four spot with very little fuss as Mohamed Salah's new Premier League goalscoring record paved the way for a 4-0 victory over Brighton.
Arsene Wenger bowed out with a victory as Pierre-Emerick Aubameyang's first-half goal secured a 1-0 win for Arsenal in their season finale against Huddersfield.
West Ham and Manchester United played out a dull goalless draw at the London Stadium -- although the result was enough to see Jose Mourinho's side secure second place in the Premier League.
Yaya Toure bade farewell to the Etihad Stadium as champions Manchester City set a hat trick of Premier League records in a routine 3-1 win over Brighton.
Jamie Vardy returned to haunt Arsene Wenger on his farewell tour as Leicester cruised past 10-man Arsenal 3-1.
Tottenham overcame a nervy night at Wembley to book their Champions League place for next season with a 1-0 win over Newcastle.
Huddersfield secured their Premier League status with a valiant 1-1 draw at Stamford Bridge which significantly dented Chelsea's slim top-four hopes.
Southampton took a huge step towards safety as a 1-0 win at Swansea inched their Welsh rivals towards the Premier League trapdoor and relegated West Brom in the process.
Arsenal gave Arsene Wenger a memorable Emirates Stadium send-off as the outgoing boss saw his side thrash Burnley.
Chelsea's Champions League hopes for next season received a boost following Sunday's narrow victory over Liverpool.
Manchester City failed to fire on the day they were presented with the Premier League trophy as Huddersfield Town claimed a vital point at the Etihad Stadium.
Tom Davies scored deep into added time as Everton salvaged a 1-1 draw against 10-man Southampton at Goodison Park, preventing their opponents from escaping the Premier League relegation zone.
West Bromwich Albion kept their slim survival hopes alive after Jake Livemore's dramatic injury time goal earned a 1-0 win against Tottenham Hotspur.
Pascal Gross scored the goal which sank Manchester United 1-0 to guarantee Premier League football for Brighton next season.
Harry Kane did his talking on the pitch as Tottenham reasserted themselves in the race for the Champions League with a 2-0 win over Watford.
Arsene Wenger was denied a point on his last visit to Old Trafford as Arsenal manager when Marouane Fellaini's injury-time header snatched victory for Manchester United.
Manchester City surpassed 100 Premier League goals for the season and left West Ham waiting to confirm top flight football next season with a 4-1 win at the London Stadium.
Chelsea's chase for a top-four Premier League spot gathered pace as Cesc Fabregas scored a landmark goal to deepen Swansea's relegation concerns.
Premier League leading scorer Mohamed Salah had a rare off day as Liverpool continue to stumble towards guaranteeing a top-four finish after a goalless draw at home to Stoke.
Manchester City celebrated their title success in style with a resounding 5-0 win over Swansea at the Etihad Stadium.
Olivier Giroud proved the scourge of Southampton once again, setting Chelsea on course for FA Cup semifinal success and a mouth-watering clash with Manchester United.
A late flurry of goals saw Arsenal secure a 4-1 win over West Ham in their first game since Arsene Wenger revealed he is stepping down as boss.
Ander Herrera has Manchester United dreaming of FA Cup glory after Tottenham Hotspur again suffered semifinal sorrow.
A late strike from Salomon Rondon helped bottom-of-the-table West Bromwich Albion come from behind to draw 2-2 against Liverpool on Saturday at The Hawthorns.