Riyad Mahrez scored his fourth goal of the season for Manchester City
Both sides had chances in an open and even first half to the game as Jack Grealish fizzed a shot just wide, while 18-year-old midfielder Lewis Hall was denied by Stefan Ortega for Chelsea.
But Mahrez struck when he drove in a free-kick early in the second half.
Alvarez sealed the win with a close-range finish soon after.
It was a deserved win for Manchester City as the eight-time winners maintained their record of never losing in the third round under Pep Guardiola.
Chelsea, however, will rue the missed chances they had in the first half, with Christian Pulisic twice denied by Ortega, while Hall should have done better with his attempt from close range, having done the hard work by making space for himself.
Hall was unlucky in the second half when his fierce first-time effort was superbly saved by the excellent Ortega.
Raheem Sterling came on midway through the second half to make his first appearance against City since leaving them in the summer.
However, he was unable to help instigate a fightback as the home side extended their winning run at Etihad Stadium to 16 games in all competitions.
The result for Chelsea, meanwhile, means they have won just two of their last seven games in all competitions and it does not get any easier for Graham Potter's side as they head to third-placed Newcastle on Saturday.
Gareth Southgate names his England squad on Thursday and while any of the performances in Wednesday night's games are unlikely to influence his decision at this late stage, he will have been pleased to see both Kalvin Phillips back on the pitch and a good performance from Grealish.
Phillips has struggled with injuries since joining City from Leeds in the summer and this appearance as second-half substitute was only his fourth of the season and his first since September.
He did not have much time to make an impression, but it will have been good for him and potentially England to get some minutes on the pitch.
Asked by Sky Sports about Thursday's World Cup squad announcement, Phillips said: "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."
Grealish, meanwhile, is likely to be in the squad for Qatar, but he has not always been able to produce the sort of performances at club level that justifies the £100m City paid Aston Villa for him in August last year.
However, this was definitely one of his best games for Pep Guardiola's side. He was creative, full of running and always showing for the ball and was unlucky not to finish with at least a goal for his efforts.
-- Courtesy of BBC Sport