Manchester: Raheem Sterling grabbed the winner as Manchester City beat Arsenal 1-0 in their Premier League clash at The Etihad and a late equaliser from Jannik Vestergaard earned Southampton a 3-3 draw away to Chelsea.
Manchester United recovered from an early own goal to beat Newcastle United 4-1 in the evening kick-off.
Liverpool were left frustrated after a 2-2 draw at Everton in the Merseyside derby on Saturday with VAR ruling out a potential winner from Jordan Henderson in stoppage time and key defender Virgil van Dijk suffering a knee injury.
Liverpool, still smarting from a 7-2 mauling at Aston Villa before the international break, got the perfect start in the third minute when Sadio Mane put them ahead, driving home a low cross from Andy Robertson.
Big blow
Centre-back Van Dijk, so central to Liverpool's defensive solidity last season, then had to go off injured after a reckless challenge from home goalkeeper Jordan Pickford.
Liverpool thought they had won the game in stoppage time through Henderson but VAR ruled that Mane was narrowly offside and the goal was chalked off.
"The picture I saw now once on the laptop, there is no armpit, there is nothing, we are just not offside," said Liverpool's bemused manager Juergen Klopp.
"Since then I had around ten interviews and everybody tells me it was not offside and that doesn't lift my mood obviously," added the German.
Everton remain top of the table on 13 points, three ahead of second-placed Liverpool.
Tactical encounter
Pep Guardiola came up against his former assistant Mikel Arteta at The Etihad and perhaps not surprisingly it was a tactical encounter won by a calm finish from Sterling.
Sterling slotted home the only goal in the 23rd minute after a Phil Foden shot was parried by Arsenal keeper Bernd Leno at the end of a flowing City counter-attack.
But City had their keeper Ederson to thank after he was quick off his line to deny Bakary Sako and Pierre-Emerick Aubameyang.
"Ederson is an incredible keeper for us," said Guardiola. "He is fantastic as a professional. He is so good. They were two incredible saves".
A late burst of goals gave Manchester United a much-needed 4-1 win at Newcastle United, with Bruno Fernandes making up for a missed second-half penalty by putting his side ahead in the 86th minute.
The visitors had gone behind to an early Luke Shaw own goal, but captain Harry Maguire put them level with a header midway through the first half and Aaron Wan-Bissaka and Marcus Rashford added goals in second-half stoppage time to complete the rout.
Southampton came from behind twice at Chelsea despite Timo Werner scoring two skilful individual goals for the home side, his first strikes in the Premier League.
Werner, who moved to Stamford Bridge from RB Leipzig in June, opened the scoring with a clever goal in the 15th minute and another in the 28th when he lobbed advancing keeper Alex McCarthy and then headed into the empty goal.
The Germany striker should have had a third in the 40th minute but he blazed the ball over the bar and three minutes later Southampton pulled one back when Danny Ings rounded keeper Kepa Arrizabalaga to score.
Southampton's positive approach was rewarded in the 57th minute when Chelsea defender Kurt Zouma misjudged a backpass and Kepa missed the ball which Che Adams blasted home.
The hosts struck back immediately with a well worked goal, the influential Werner crossing for Kai Havertz to earn his own first Premier League goal with a simple tap-in.
But the Saints struck again in added time to leave Frank Lampard concerned about the errors his Chelsea team made.
"We can do better... We need to be more solid and making individual mistakes gives other teams chances," he said.
