Former Chelsea midfielder Mateo Kovacic scored a stunning late goal to ensure Manchester City took all three points at Stamford Bridge on Sunday.
Premier League Golden Boot winner Erling Haaland had earlier carried on where he left off last season by scoring the opener to set City on their way.
It meant a losing start for new Chelsea manager Enzo Maresca in his first league game in charge of the club.
The Italian, who led Leicester City to promotion back to the top flight last season, also had to answer questions before the game over his decision to leave Raheem Sterling out of his squad.
Haaland opened the scoring for City after 18 minutes when Bernardo Silva flicked a Jeremy Doku cross into the box and the Norwegian outmuscled Marc Cucurella before dinking the ball over keeper Robert Sanchez.
Pep Guardiola had switched Doku to the left side shortly before the goal. There was a lengthy VAR check but Silva was just played onside by Wesley Fofana in the build-up. It was Haaland's 13th goal in nine Premier League games in August.
Enzo Fernandez had a penalty shout for Chelsea denied just past the half-hour mark when he went down too easily under a challenge from Savinho after allowing the ball to escape him with a poor first touch.
After impressing on his debut for City in the Community Shield win over Manchester United, the 20-year-old Brazilian winger again looked excellent on his Premier League bow, showing pace, control and the ability to deliver dangerous crosses.
Doku and Silva forced good saves from Sanchez and Chelsea wasted several decent chances before Nicolas Jackson thought he had scored after 44 minutes.
A Cole Palmer shot from the edge of the area was spilt by Ederson into the path of the onrushing Jackson, who tucked it into the back of the net but the striker had strayed marginally offside before making his run into the box.
Chelsea then had another penalty appeal ruled out as Fernandez threw himself down after minimal contact in the box from Ruben Dias but it was waved away by referee Anthony Taylor. Shortly afterwards, the official also rejected a third penalty appeal after Nkunku went over when his run was blocked by Rico Lewis.
After the restart, Haaland was teed up well by Silva but his tame shot was saved easily by Sanchez.
Chelsea's new £54 million signing from Wolves Pedro Neto almost made an immediate impact when he came on as a substitute for Nkunku in the 58th minute.
As Fernandez squared the ball in the six-yard box, the Portuguese was denied the chance to poke it home by a last-ditch clearance by Rico Lewis.
Lewis then had the ball in the back of the net for City before it was chalked off for a foul by Haaland in the build-up.
Maresca rang the changes, bringing on fresh legs in 18-year-old striker Marc Guiu, signed for £5m from Barcelona, and fellow debutant Kiernan Dewsbury-Hall on 67 minutes in place of Jackson and Romeo Lavia.
The home side began to put City under pressure and a Malo Gusto cross that hit Mateo Kovacic's arm was ruled not to be a penalty under the new interpretation of the law brought.
Another of Chelsea's summer signings, Portuguese Renato Veiga, was brought on to replace a limping Cucurella.
But the game was taken away from the home side after 84 minutes when Croatian midfielder Kovacic chested the ball down and broke clear before scoring from 25 yards out. Sanchez, who got a glove to it may have felt he could have done better.
While the defending champions got their quest for a fifth straight title off to a winning start, new Chelsea boss Maresca will know he has plenty of work to do to fashion a team that can threaten Premier League's top four.
Afterwards Maresca told Sky Sports: “I think we competed very well for much of the game. The performance was there but we didn’t take the chances.
“We were against the champions today. They are a master in this kind of moment. We don’t like to lose. We just need to continue.”
There has been plenty of talk about the Blues’ unwieldy squad in the build-up to the season and Maresca’s decision not to include Sterling in his squad raised questions.
Sterling’s representatives said in a statement issued before the match: “[Raheem] has had a positive pre-season under the new coach, who he has developed a good working relationship with.
“As a camp, we have always had positive dialogue with, and assurance from, Chelsea FC in relation to Raheem’s future at the club, so we look forward to gaining clarity on the situation.”
Asked about his decision, Maresca said: “The manager has to make some decisions. Sometimes players don’t like it. Just a technical decision, no more than that.”
City manager Guardiola said when asked about Rodri’s injury absence: “Rodri is massively important for us so it’s important to have Mateo [Kovacic] here because he is an experienced player and a great person. He made a good performance.”
