The Blues were under pressure for most of their match with Pep Guardiola's team, but their grit in the face of adversity saw them through
David Luiz felt Chelsea's humility was the key to them defeating a Manchester City team he thinks are "the best in the world".
City were in control from the outset at Stamford Bridge but they fell behind against the run of play when N'Golo Kante steered Eden Hazard's pass into the roof of the net.
Pep Guardiola's decision to play Raheem Sterling through the middle did not work out, while the introduction of Gabriel Jesus in the 53rd minute failed to improve matters.
Chelsea remained solid at the back in the second period and David Luiz ended City's 14-game unbeaten run in away Premier League matches 11 minutes from time.
The Brazilian was proud of the way the Blues dug in to become the first side to beat the reigning champions in the top flight this term.
"It was a great game, and to be honest, we were playing the best team in Europe, or the world at the moment," David Luiz told BT Sport.
"They have been together for more than three years, they play really, really well and have great players, so we were set to suffer.
"We had a lot of humility and tried to take our chances to score. We did our plan well, it was a great game.
"All the team did great, we have tried a lot this season to improve. We have had some bad results and like I said, the humility was the key today. I think all the team did great.
"We keep on fighting with humility, feet on the ground and try to improve every day."
Maurizio Sarri has moved Kante out of his deep-lying midfield role this season and called on the World Cup winner to score more.
While the France international was pleased to double his tally for the campaign with the opener, he is not fixated with trying to be more prolific.
"The most important is to give my best on the pitch, to play with my team-mates. I'm happy when I can be on the scoresheet and I'm happy to score my second goal of the season," said Kante.
"Manchester City are a very good team. I think we had some difficult moments in the game, but we were able to suffer together, to make the effort together. We are happy for the win."
Bohcimrt
146
On this super Sarriday evening, the Sarriboys made my day when they simply strolled past Pepcity's walking dead. After the Sarriball had been stolen by Tottenham and Wolves narri a single Sarri-fan expected them, not only to recover it but also to do it in such Sarri-style, with a couple of great Sarri-goals. Whatever Sarri smokes, he must have shared it with his boys before the match. In that case we say, "Keep on smoking!!!"
Nesaiknruy_Legend
122
The 2 losses improved us cos it woke us up to the reality of the premier league. And City got the same wake up call today. Soon come Liverpool will also get humbled. The prem isn't easy that you win every time. Invincible was a fluke season and there were a lot of questionable decisions in that season anyway. Premier league is the most competitive league by a country mile..... 6 teams that have an equal chance and each one has something with which they can beat another one.... like we lost to Spurs, who lost to Arsenal, who lost to City, who lost to us. That competitive aspect and unpredictability is what makes it the best and most enjoyable to watch....