The defeat left the London side further adrift from the UEFA Champions League qualification spots.
Pep Guardiola’s side, who have now won 14 straight home games, need just four wins from their remaining nine matches to be crowned champions.
“It was so important, a win today is another step closer,” Guardiola said.
“We need four victories to be champions. It is in our hands and if our behaviour is like today we will be champions”.
After Chelsea’s defensive approach resulted in a first-half stalemate, Manchester City went ahead 33 seconds into the second period when Bernardo Silva turned in a low cross from David Silva.
Chelsea have now lost four of their last five Premier League games and are in fifth place, five points behind Tottenham Hotspur who occupy the fourth Champions League spot.
It was far from a classic game with Chelsea showing little ambition and Manchester City happy to play within themselves for large stretches.
But that was perhaps a consequence of a title race that has effectively been over for months.
Still Chelsea hardly approached the game like a team who needed points to get back in contention to qualify for Europe’s elite competition.
Antonio Conte left both Chelsea’s recognised strikers — Alvaro Morata and Olivier Giroud — on the bench and opted to play winger Eden Hazard as a lone striker.
Conte defended his approach, saying he was concerned about the risk of a heavy defeat.
“When you play against a team that has shown to be stronger than you — because 25 points is a big difference — you have to think with your brain and not your head.
“Otherwise, you finish with a bad loss and that’s not good for the players,” he said.
The Londoners defended deep and in numbers from the outset but, missing the tenacity of the absent N’Golo Kante, showed little willingness to press in midfield.
The result was a first half dominated by Manchester City possession but with few openings.
Manchester City, who had played against Arsenal on Thursday, lacked their usual sharpness in midfield.
They went close to an opener when a deep cross from Kevin De Bruyne was brilliantly taken down by Leroy Sane.
But the German’s goalbound shot was cleared off the line by Cesar Azpilicueta.
Nicolas Otamendi put the ball in the net for Manchester City, after Sergio Aguero had hooked on a quick free-kick.
But the effort was ruled out for offside and the teams went in for halftime with a disappointing game scoreless.
It took just 33 seconds of the second half for that to change, however.
Aguero found David Silva on the left and the Spaniard’s low cross was turned in at the back post by Bernardo Silva.
If Chelsea fans expected that goal to force a change of approach from Conte, they were disappointed.
They had to wait until the 78th minute for Giroud to be brought on for Willian.
But neither the French forward nor Morata, who came on in the final minute, made an impact.
Only an optimistic effort from Marcos Alonso in stoppage-time which flew wide troubled Manchester City’s underworked defence.
Manchester City completed 902 passes, more than any other team in a single Premier League match since 2003-04 when such statistics were first officially recorded.(Reuters/NAN)