It was probably the final nail in the coffin for City however, who are now a massive 14 points behind Chelsea in the league.
Chelsea took the lead in the 10th minute when Eden Hazard’s strike at goal glanced off the head of returning City skipper Vincent Kompany and into the goal.
Although it took it slight deflection, Willy Caballero should really have done better.
But another goalkeeping error, this time from Chelsea’s Thibaut Courtois, saw the visitors back in the game.
Courtois’ kick-out went straight to David Silva. The Spaniard fired an effort at goal that Courtois could only parry out to Sergio Aguero, and he tapped home for 1-1.
But Premier League pace-setters Chelsea ensured they went in at the break ahead. Fernandinho tripped Pedro in the box, and although Hazard saw his original penalty saved, he scored from Caballero’s parry out.