Sarri's side put the midweek disappointment of losing to Wolves behind them to get back to winning ways and bring City's unbeaten start to the season to an abrupt end.
The Metropolitan Police said no arrests had been made but they were also looking at the incident.
After defeats by Tottenham Hotspur and Wolverhampton Wanderers in their last three matches after going unbeaten in their opening 12 league games, it was a return to form for Chelsea after the first serious questions had been asked of new manager Maurizio Sarri.
The 24-year-old, who celebrated his birthday on Saturday, has been a player for Manchester City since 2015.
Yet, for all City's possession, the visitors were stung by a sucker punch just before half-time as Sarri's decision to field Eden Hazard as the focal point of the Chelsea attack and maintain Kante in an advanced midfield role paid off.
"I like it, because I played it a year ago also, so I know what to do, but the feeling is a bit unusual because you don't touch the ball a lot", Hazard added. For me is not easy to win against Guardiola.
"We won today but I think we have to say we were a bit lucky in the first 25 minutes, because they could have scored".
Mohamed Salah was back to his devastating best with a hat-trick, but then showed the spirit evident in Jurgen Klopp's squad when he handed his man of the match award to team captain James Milner, who had filled in at right-back in what was his 500th Premier League appearance.
The result means we now sit second in the table, one point behind new leaders Liverpool.
Defending set-pieces has often been a rare Achilles heel for City and it was exposed when Luiz made the game safe by rising highest to Hazard's corner and looping a header in off the underside of the bar. "It is emotional for me to see these players do what they do every three days".
"The most important is to give my best on the pitch, to play with my team-mates. It can help the team". "He was in the box for the first goal but I think today he played in the right position, close to Jorginho". Chelsea is up to third but now sits eight points back of Liverpool.
Guardiola, however, still liked what he saw, believing Chelsea simply took their chances at key moments.
"It was a fantastic game but this has overshadowed it and that's what we don't want".
United took advantage of Bournemouth's defeat and Everton not being in action till Monday to rise up to sixth by ending a four-game winless run in the league with a comfortable victory over bottom club Fulham. To be where we are - we should be proud.