Chelsea are currently fourth in the league with 34 points from 16 games
Chelsea inflicted Manchester City's first loss of the Premier League season on Saturday, winning 2-0 as the champions were replaced by Liverpool in top spot.
After losing two of its last three league games, Chelsea was forced to repel waves of City attacks before N'Golo Kante scored from the team's first shot on target in the 45th minute.
Buoyed by going in front, Chelsea controlled the second half and David Luiz headed the hosts further in front in the 78th.
It ended City's 21-game unbeaten run in the league stretching back into last season when Pep Guardiola's side won the title with 100 points.
"They had minimum chances and scored," Guardiola said. "It is emotional for me to see these players do what they do every three days. It is the level that it is. We were outstanding except for five (or) eight minutes."
Liverpool moved a point ahead of City after beating Bournemouth 4-0 earlier Saturday with Mohamed Salah scoring a hat trick. Chelsea is eight points behind Liverpool.
City was without key players Kevin De Bruyne and Sergio Aguero at Stamford Bridge and manager Guardiola may have further injury concerns to contend with. With the busy festive period approaching, midfielder Fernandinho required treatment in the first half before the influential David Silva limped off with an apparent hamstring issue in the second half.
For all of their possession and pressing in attacking areas, City created little and couldn't recover from conceding. While the visitors had a handful of decent openings, they failed to register a meaningful attempt on goal until Gabriel Jesus' effort in injury time.
Strikers were conspicuous by their absence, with Hazard and City's Raheem Sterling deployed in the false nine position.
Maurizio Sarri explained his deployment of Hazard, without a goal in 11 matches for club and country, as being for "faster football." The Belgian showed his class in the crucial moments of the match by creating both goals.
Chelsea struck on the counter-attack. Luiz's long ball found Pedro Rodriguez, whose crossfield ball to Willian did not create the intended shooting chance. Willian found Hazard, who slid the ball through for the late-arriving Kante to blast in for his second league goal of the season.
The second came from a set piece. Hazard's inswinging corner was met by Luiz, who rose highest to send a looping header into the net off the underside of the crossbar.
