Liverpool produced their regular party trick, leaving it late before securing all three points against Crystal Palace while Manchester City had to dig deep to see off Frank Lampard's vibrant Chelsea.
Elsewhere, second-placed Leicester kept the gap to leaders Liverpool to eight points with a 2-0 win at Brighton while Jose Mourinho started his career as Tottenham boss with victory at West Ham.
Manchester United looked set to leave Bramall Lane with a victory after a helter-skelter match but a late Sheffield United equaliser meant they had to settle for a 3-3 draw.
Here, AFP Sport looks at three things we learned from the Premier League weekend:
Lampard's Chelsea come of age
It's one thing to beat Crystal Palace and Watford as you climb the Premier League table but it's quite another to go toe to toe with the champions on their own turf.
Lampard's young team started Saturday's match at the Etihad one point and one place above their illustrious opponents.
The Londoners were the better side in the early stages of the game and deservedly took the lead before Pep Guardiola's men battled back to win 2-1 and stay nine points behind Liverpool.
A measure of Chelsea's achievement is that City's possession figure of 46.74 percent was the lowest recorded by a side managed by Guardiola in any of his 381 top-flight matches in charge.
"I don't think you can come away from that game and say it was anything other than two really strong teams going against each other," said Lampard, whose side are now fourth.
"One wins it because of a deflected goal and a really good goal, and the rest was in the balance."
Is the 'real' Dele Alli back?
Jose Mourinho made one of his first priorities at Tottenham bringing back the "real Dele Alli" and the midfielder did not disappoint his new boss.
"I asked him if he was Dele or Dele's brother," Mourinho explained ahead of Saturday's Premier League match at West Ham.
"He told me he was Dele. 'OK,' I said. 'Play like Dele'."
Injuries and poor performances have seen Alli fall out of the reckoning with England but the new coach has plans to reinvigorate the 23-year-old and he was delighted with his performance at the London Stadium.
Alli set up Son Heung-min's opener in a 3-2 win for Tottenham -- their first away victory in the Premier League since January.
"He was the old Dele Alli, the Dele Alli of a couple of years ago, that impressed not just England, but the world. He did exactly what I wanted him to do, with two days of work," said Mourinho.
"With important selection of information I tried to make clear for him exactly the spaces where we wanted him to play, offensively and defensively. He is an intelligent footballer to understand what we wanted and very, very important for the team. I am really pleased with his performance."
Mauricio Pochettino last week became the second managerial casualty in the Premier League this season following the earlier dismissal of Watford boss Javi Gracia.
A number of bosses will now be fretting that they could be next, including Everton's Marco Silva, Arsenal boss Unai Emery and West Ham manager Manuel Pellegrini.
A 2-0 home defeat for Everton against struggling Norwich made it six losses in nine league matches and left the Toffees just four points above the relegation zone.
It was reported that majority shareholder Farhad Moshiri held talks with fellow directors after the game to discuss the growing crisis.
Things look bleak for Silva with a horrendous set of fixtures coming up over the next few weeks. Everton face Liverpool, Leicester (twice), Chelsea, Manchester United, Arsenal and Manchester City.
Former Manchester City boss Pellegrini has seen his West Ham side plummet down the table after losing five out of six league games following a promising start to the season.
Arsenal are still in the upper reaches of the table but are going nowhere, with just two wins from their past 11 Premier League games.
Emery was publicly backed by the Arsenal hierarchy at the start of the international break but the pressure will continue to grow unless he can turn things around following their fortuitous 2-2 draw with struggling Southampton.
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