"It was a great game and we have to be honest playing against the best team in Europe or the world at the moment," Luiz said. "They have great players, so we had a lot of humility and tried to take our chances to score, so we did our plan well."
Not only did City lose for the first time in the league this season but they also lost top spot to Liverpool, who moved a point ahead after Mohamed Salah's hat-trick inspired a 4-0 victory at Bournemouth.
Chelsea still have much work to do to move back into contention. Having lost two of their last three league games before City's visit, Maurizio Sarri's fourth-placed side are eight points behind Liverpool.
Tottenham remain two points ahead of Chelsea in third and six points from top spot after winning 2-0 at Leicester City.
The visit of last-placed Fulham allowed Manchester United to end a four-match winless run as Jose Mourinho's side claimed a 4-1 victory.
Ashley Young struck into the top corner to put United ahead in the 13th minute, Juan Mata slotted in from Marcus Rashford's cutback in the 28th and Romelu Lukaku ended his 997-minute wait for a goal at Old Trafford in the 42nd.
Substitute Aboubakar Kamara's penalty reduced the deficit from the spot but Fulham midfielder Andre-Frank Zambo Anguissa's sending off in the 68th was followed by Marcus Rashford netting for United in the 82nd. The title remains far from United's thoughts, with Liverpool 16 points ahead.
For the first time this season, Salah scored more than once in a league game. It's a reminder of how he won the Golden Boot last season.
At Bournemouth, Salah broke the deadlock in the 25th minute when he responded to a parried shot. The Egyptian stayed on his feet under a challenge from Steve Cook before drilling home in style, then netting three minutes into the second half.
Cook somehow back-heeled past his own goalkeeper, Asmir Begovic, when trying to clear Andy Robertson's cross. A mazy dribble preceded Salah completing his hat-trick in the 77th minute.
All Whites striker Chris Wood played the full 90 minutes for Burnley, who beat Brighton 1-0 for their third win of the season to climb out of the bottom three. James Tarkowski chested in the 40th-minute winner, deflecting in a Jack Cork shot.
- AP