Arsenal moved level on points with leaders Manchester City, while Tottenham maintained their revival.
AFP Sport looks at three talking points from the weekend's action:
Walls closing in on Carrick
Michael Carrick's future as Manchester United boss was already hanging by a thread before Bournemouth inflicted what is likely to be a brutal last act for the former England midfielder at Old Trafford.
For the third time in four seasons, the Cherries rolled out of the 'Theatre of Dreams' as 3-0 winners.
Carrick made a stand by dropping Bruno Fernandes after the United captain's outspoken criticism of his tactics in a 4-1 Champions League drubbing by Como on Wednesday.
Fernandes may not have hit the heights of his player of the season performances last season, but this display showed a United squad short on quality can ill afford to live without their best player.
Individual mistakes by Leny Yoro and Senne Lammens gifted Bournemouth's second and third goals, but there was little sign of a collective resilience from United as their winless run stretches to eight games.
The biggest ovation of the day from the home fans was reserved for Carrick as he departed down the tunnel in what could be a farewell for another United great chewed up and spat out by the seemingly impossible job.
Carrick's exit appears inevitable, but 13 years and seven managers on, United are no closer to reversing a fall from grace that began with Alex Ferguson's retirement after their most recent English title.
Set-pieces back in fashion for Arsenal
Mikel Arteta believes Arsenal have rediscovered their potency from set-pieces after breaking their duck in Saturday's 2-0 win against Everton.
The Gunners developed a reputation as set-piece specialists last term, scoring 29 times from corners, free-kicks and penalties en route to winning the title.
But Ezri Konsa's scrambled opener against Everton at the Emirates Stadium marked the first time the champions had scored from a set play in eight top-flight games this campaign.
"We hadn't scored from a set-piece, which we were disappointed with because we had generated so many chances as well," Arteta said.
"I'm sure that's going to unlock something and that belief of the players. So they are really convinced.
"You have to see them when we train the level of attention and how much they believe in what we do and what Nico (Jover, set-piece coach) does as well."
Konsa's first goal for the club, following a Martin Odegaard corner, put Arsenal on course to move level on points with leaders Manchester City, who were beaten 2-1 at Aston Villa to end their 100 per cent in the top-flight this term.
Spurs love affair
Jan Paul van Hecke said Tottenham manager Roberto De Zerbi has earned the love of his players after their 2-0 victory at Chelsea on Saturday.
Van Hecke produced a towering display in central defence to help Tottenham win at Stamford Bridge for only a second time in the Premier League era.
An own goal from Blues keeper Mike Penders' own-goal was followed by a superb solo effort by Mathys Tel to end Tottenham's wretched record at a venue that had turned into their personal house of horrors.
"Everyone is buzzing. Massive result, I think fully deserved. We played some really, really good football," Van Hecke said.
Tottenham had endured a slow start after a summer of lavish spending, with Van Hecke one of 10 players signed for a combined £380 million.
De Zerbi's side beat Coventry to banish their winless start to the league season before putting Chelsea to the sword.
"He's loved," Van Hecke said of De Zerbi. "I love him as well. He's a top manager and everyone's really happy here."