It was talisman Kevin De Bruyne who made the difference with a beautifully crafted shot from the outside of the box after 70 minutes.
City has now won 12 league games in a row and looks strong to defend its Premier League title.
Chelsea remains in second with Liverpool one point behind with two games in hand -- Jurgen Klopp's side now looks like the only side that could challenge Pep Guardiola's title defense.
"We will not give up but if Manchester City keeps winning every game, no one can stop them," Chelsea manager Thomas Tuchel said after the match.
'Momentum can change'
City looked impressive throughout with its star players, such as De Bruyne and Raheem Sterling, turning up for the big game against their title rivals.
Chelsea may have looked passive for large parts of the match -- it failed to register a shot on target in the first half -- but Tuchel's side had chances to claim all three points.
The best fell to Romelu Lukaku who saw his curled effort brilliantly saved by goalkeeper Ederson with the scores still level.
Jack Grealish had spurned City's best chance of the match in the first half but De Bruyne saved his blushes with a superb effort from a distance with just 20 minutes remaining.
"It's nice to score, it was important as it was the only one. We knew if we won we would make the gap bigger," De Bruyne said after the game.
"I got away from N'Golo Kante at the right time, I was looking at the space and they were dropping off, I found the angle and it worked perfectly.
"We have been in this situation before, things can change and momentum can change. The team was focused on what we could do today."
Liverpool has the chance to make a dent in City's lead at the top of the table when it faces Brentford on Sunday.
Klopp's side will need a near-perfect end to the season if it has any chance of catching Manchester City.
"If Liverpool wins their games in hand it is eight points, so my job is to take out of the heads of the players what people will say," Guardiola said when asked about the title race.
"We are more than pleased but there is a lot of a job to do."