After losing to Liverpool a fortnight ago, City faced the prospect of falling 12 points behind the Premier League leaders as N’Golo Kante shot Chelsea into an early lead at the Etihad Stadium.
But City powered back to win 2-1 with both goals coming before the interval, the first a deflected strike from De Bruyne and the second a superb solo effort from Riyad Mahrez.
The result saw City, who also hit the woodwork through Sergio Aguero and had a late Raheem Sterling goal disallowed by VAR for a marginal offside, leapfrog Chelsea to go third.
De Bruyne said: “We work really hard and the main thing, when you lose a game, is to come back with a good reaction.
“That’s what we have always done over the last four or five years. I think it’s very rare to see us lose two games in a row.
“We work hard as a team and that’s what we did. We have a lot of quality to make the difference.”
City are now waiting for updates on the fitness of record goalscorer Aguero, who limped off late on with a muscular problem manager Pep Guardiola admitted “doesn’t look good”.
Chelsea, who had won their previous six games, made life tough for Guardiola’s men. City’s 46.7 per cent possession was remarkably the lowest amount a Guardiola side has had in any of the Spaniard’s 381 top-flight matches as a manager.
De Bruyne said: “We knew before the game that there would be moments where we would have trouble to get the ball.
“Everyone knows we are a team with a lot of quality with the ball but we showed we can also do the other side, with good defending.
“It’s hard to get the ball, but I think we created more chances.”