A 46th minute goal from Bernardo Silva was enough to secure a deserved victory and moved City 18 points clear at the top of the table.
It also rounded off a magnificent week for the club with City lifting the Carabao Cup last Sunday, then crushing Arsenal 3-0 at the Emirates last Thursday.
And David, who captained the side against Antonio Conte's reigning champions and produced another sublime individual display, said the significance of the result wasn't lost on the club.
"It’s the same three points but we may be another step closer towards the Premier League title," said the Spanish midfield maestro.
"It felt like a significant win. When you play the champions you know they play well and defend so well.
"We couldn't find space at the beginning but then Bernardo scored his goal.
"It's the same three points whether you score one, two or three goals so we are very happy.
"It was a difficult week with three games but we won the Carabao Cup and we have got two league wins to take us closer to the Premier League.
"We knew we had to be patient as they close the space very well but we scored and we are very happy."
Goalscorer Bernardo maintained his own excellent form, rounding off his performance with another crucial goal but insisted the Blues would not lose their focus or concentration.
"We know the way Chelsea play but we wanted to be aggressive and dominate from the first minute and I think we did that,"said Bernardo.
"It’s a very good three points but we have to keep going in the league and in the Champions League."