Chelsea came out on the front foot, with surging attacks which took City's confused defence by storm. It was, however, their first real chance that gave them the lead, with Azpilicueta pulling the ball back to the penalty spot for Hazard to fire past Willy Caballero, who should have done better.
City recomposed and took full control of the ball. Their equaliser came after a howler from Courtois, who gave the ball straight to Silva to drive into the box. The keeper then saved his shot, but the rebound fell to Aguero who tapped into an empty net to level the score.
The visitors continued to dominate the game, but it was Chelsea who would reclaim the lead. There were no complaints after Pedro was pulled down by Fernandinho in the box. Hazard took the penalty to the keeper's left, Caballero saved but the rebound fell to the Belgian to fire in his second.
The second half began along the same lines. Manchester City were comfortable on possession, while Chelsea offered close to nothing in attack. Lacking in creative play, they put on a strong defensive display, not allowing the visitors to get clear chances on goal.
Willian came on for the Blues with 15 minutes to go, and they seemed to take a step forward, coming closer to Caballero. City, at this stage, were unable to get hold of possession and grew frustrated as Chelsea gave a masterclass at seeing a game out.
With this victory, Conte's men edge even closer to winning the Premier League, despite Tottenham taking the three points at the Liberty Stadium and maintaining the 7-point gap.