Liverpool deepened West Ham United's problems as they strolled to a 4-1 win at the London Stadium.
Peter Crouch's second-half header earned Stoke a point at home to Leicester and ensured a familiar scoreline at the bet365 Stadium.
New boss Claude Puel began his Leicester reign with a routine win over managerless Everton as the Foxes eased away from trouble.
Eden Hazard's first Premier League goal of the season eased Chelsea past Bournemouth 1-0 at Dean Court.
Leaders Manchester City strolled past West Brom to maintain their grip at the top of the Premier League.
Liverpool manager Jurgen Klopp got one over on best friend David Wagner as Daniel Sturridge's 100th club goal paved the way for a 3-0 win over Huddersfield at Anfield.
Arsenal came from behind to beat Swansea in Arsene Wenger's 800th Premier League game in charge of the Gunners.
Anthony Martial came off the bench to score the winning goal as Manchester United beat Tottenham 1-0 at Old Trafford.
West Ham eased the pressure on manager Slaven Bilic by fighting back from two goals down to beat Tottenham 3-2 in the Carabao Cup fourth round.
David Unsworth's first match as Everton's caretaker manager ended in a 2-1 defeat at Chelsea in the fourth round of the Carabao Cup.
Claudio Bravo was the hero as stuttering Manchester City needed penalties to see off hard-working Wolves and make the Carabao Cup quarterfinals.
Teenage striker Eddie Nketiah came off the bench to score twice on his home debut and send Arsenal into the quarter-finals of the Carabao Cup at the expense of Norwich.
Manchester United bounced back from their Huddersfield horror show with a comfortable Carabao Cup victory at Swansea.
Harry Kane scored twice as Tottenham Hotspur brushed Liverpool aside 4-1 at Wembley on an afternoon of glaring defensive frailty from Jurgen Klopp's visitors.
The pressure on Everton manager Ronald Koeman increased as his side dropped into the relegation zone after a 5-2 defeat to Arsenal at Goodison Park.
Sergio Aguero equalled Manchester City's goal-scoring record as the Premier League leaders saw off hard-working Burnley 3-0 at the Etihad Stadium.
Huddersfield are celebrating one of their best wins in decades after Aaron Mooy and Laurent Depoitre brought Manchester United's unbeaten Premier League start to a shock halt.
Michy Batshuayi came off the bench to score twice as Chelsea fought back from behind to win a six-goal thriller against Watford.
A late Wayne Rooney penalty snatched a 1-1 draw for Everton at Brighton.
Manolo Gabbiadini's double rescued Southampton as his side twice came from behind to salvage a 2-2 Premier League draw against Newcastle.
Arsenal gave away a lead to lose 2-1 away to Watford as Tom Cleverley netted an injury time winner.
Tottenham are finally off the mark at Wembley after Christian Eriksen sealed a narrow win over Bournemouth and his side's first Premier League victory under the arch.
Kevin De Bruyne orchestrated a Manchester City masterclass as Pep Guardiola's freescoring side thrashed Stoke 7-2 at the Etihad Stadium.
Crystal Palace deservedly claimed a first Premier League win of the season with a 2-1 victory over champions Chelsea at Selhurst Park.
Liverpool versus Manchester United again failed to live up to the hype as Jose Mourinho's safety-first policy saw him once more frustrate the hosts at Anfield.
Joselu handed Newcastle boss Rafael Benitez a draw against former club Liverpool as missed chances cost the visitors dearly.
Arsene Wenger celebrated his 21st anniversary as Arsenal manager with a 2-0 win over Brighton and a brilliant team goal scored by Alex Iwobi.
Manchester City demonstrated their Premier League title credentials with a dominant 1-0 victory at champions Chelsea.
Marouane Fellaini's first Manchester United brace helped Jose Mourinho's men to another comprehensive victory, leaving Crystal Palace reeling from a seventh straight Premier League defeat without a goal.
Harry Kane stole the show as Premier League title challengers Tottenham cruised to a 4-0 win over Huddersfield at the John Smith's Stadium.
Manchester United have reached an agreement with Shakhtar Donetsk for the transfer of Brazil international midfielder Fred, the Premier League club confirmed on Tuesday.
Stephan Lichtsteiner has become Unai Emery's first signing for Arsenal after joining the Premier League side on a free transfer from Juventus.
Frank Lampard has been appointed the new manager of Derby County on a three-year contract, with former Chelsea academy coach Jody Morris as his assistant.
Liverpool have announced a deal to sign Brazilian midfielder Fabinho from Monaco.
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.