City winger Riyad Mahrez broke the deadlock on 52 minutes with a well-taken free-kick, and forward Julian Alvarez doubled City’s lead shortly after when he converted a rebound from Mahrez’s shot.
United States forward Christian Pulisic started and played the full match, with his best opportunity coming in the opening stages, although he failed to make the most of it as he mishit a rolling ball across the box.
The result means City’s search for their fifth Carabao Cup title in six seasons continues, while Chelsea, who were beaten in last year’s final against Liverpool, are sent crashing out in the third round.
Kalvin Phillips, who has struggled with injuries since joining City last summer, made a return from off the bench on 50 minutes and will be watching with eager eyes when England boss Gareth Southgate names his squad for the World Cup on Thursday.
When asked about the squad announcement, Phillips told Sky Sports: “Anything can happen. I’m optimistic but I know with the amount of game time I’ve had there’s always a doubt.
“I think with my injuries I’ve not been playing 100% because of my shoulder. Now it’s sorted I can get back to what I was before. Hopefully it’ll put me in good stead.”