Tottenham kept their Premier League title ambitions alive by staging an extraordinary late show at relegation-threatened Swansea.
Liverpool let a lead slip away late on to draw 2-2 against Bournemouth and miss the chance to strengthen their grip on third place.
Arsenal returned to winning ways with a solid victory over West Ham as a fifth straight defeat plunged Slaven Bilic's side deeper into the fight for Premier League survival.
Leicester piled the misery on David Moyes and pushed Sunderland closer to relegation from the Premier League with a gritty 2-0 win.
Manchester United drew yet another league match at Old Trafford -- but the overriding emotion at the final whistle was relief rather than frustration after Zlatan Ibrahimovic struck a stoppage-time penalty against Everton.
Arsenal twice came back from a goal down to ease some of the pressure on manager Arsene Wenger in an entertaining 2-2 draw at the Emirates.
Crystal Palace stunned Chelsea with a 2-1 win to give the Blues' Premier League title rivals hope and their survival prospects a major boost.
Tottenham Hotspur cut Chelsea's lead at the Premier League's summit to seven points after becoming only the fourth top-flight side to win at Burnley this season.
Manchester United stumbled at a crucial time in the race for the top four as well-drilled West Brom became the latest side to hold Jose Mourinho side to an Old Trafford draw.
Leicester edged closer to certain Premier League safety as boss Craig Shakespeare entered the record books after a routine win over Stoke.
Liverpool moved into third place in the Premier League as they comfortably beat neighbours Everton 3-1 in the Merseyside derby at Anfield -- but were hit by an injury to Sadio Mane.
Manchester City and Liverpool had to settle for a point each in their battle for Champions League qualification after a thrilling 1-1 draw at the Etihad Stadium.
Jesse Lingard's thunderous strike lit up what ended up being a nervy Manchester United win as relegation-threatened Middlesbrough rallied under caretaker boss Steve Agnew.
Tottenham Hotspur moved back to within 10 points of Premier League leaders Chelsea as they saw off Southampton 2-1 at White Hart Lane on Sunday -- their 10th home league win a row.
Chelsea's march towards the Premier League title continued as they extended their lead to 13 points thanks to Gary Cahill's 87th-minute winner at Stoke.
Leicester made it four wins from four under Craig Shakespeare and picked up their first away victory of the season with a 3-2 success at West Ham.
Craig Dawson's double piled more pressure on Arsenal boss Arsene Wenger as the Gunners lost 3-1 at West Bromwich Albion.
Antonio Conte and Jose Mourinho had to be separated as N'Golo Kante's strike sent Chelsea into the FA Cup semi-finals with a 1-0 win over Manchester United at Stamford Bridge.
Liverpool consolidated fourth spot in the Premier League with a come-from-behind 2-1 home victory over Burnley.
Son Heung-Min's hat trick fired Tottenham into the FA Cup semifinals but their 6-0 demolition of Millwall was marred by racist chants towards the South Korean from visiting supporters.
Manchester City eased into the FA Cup semifinals as they produced a dominant display to win 2-0 at Middlesbrough.
Arsenal scored four second-half goals as they ended non-league Lincoln City's outstanding FA Cup run with an emphatic 5-0 victory at the Emirates Stadium.
Romelu Lukaku drew level with Harry Kane in the race for the Premier League's golden boot as Everton coasted against West Brom for their fifth straight home Premier League win.
Stoke frustrated Manchester City as they held out for a goalless draw in their re-arranged Premier League clash at the Etihad Stadium.
Eden Hazard and Diego Costa were on target as clinical Chelsea swatted aside West Ham 2-1 to take a 10-point lead at the top of the Premier League.
Sergio Aguero struck for the fifth time in three games as Manchester City eased past relegation-haunted Sunderland and back into third place in the Premier League.
Harry Kane won his top-scorer tussle with Romelu Lukaku by bagging a brace as Tottenham held on for a 3-2 victory over Everton.
Liverpool put their disappointing defeat at Leicester behind them to move up to third place in the Premier League with a 3-1 home win over Arsenal, who dropped to fifth.
Leicester continued to breathe new life into their Premier League survival bid under the guidance of Craig Shakespeare as he strengthened his claims for the manager's job with victory against relegation rivals Hull.
Zlatan Ibrahimovic had a second-half penalty saved as Manchester United were held 1-1 by Bournemouth and missed the opportunity to move ahead of Liverpool and into fifth in a feisty game at Old Trafford.
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.