City had plenty of chances in the first half - Kalidou Koulibaly nearly turned Jack Grealish's delightful through ball into his own net in the 6th minute.
Ortega made a superb stop at the other end to deny Christian Pulisic in the 23rd minute after the American ran from his own half.
Grealish went close in the 41st minute but found his curled effort denied by Chelsea goalkeeper Edouard Mendy.
Blues youngster Lewis Hall had a golden opportunity in the 44th minute and was the star of the show throughout the first 45 minutes.
The English teenager shrugged off Rico Lewis but could only place directly at the onrushing City stopper Stefan Ortega.
City made the breakthrough in the 53rd minute, and it was Riyad Mahrez whose exquisite free-kick beat Mendy to put Pep Guardiola's side ahead.
Chelsea immediately responded two minutes later when Hakim Ziyech curled an audacious effort into the far corner, but Ortega was on hand to tip it away.
From the resulting corner, Ziyech had another pop at goal, but his powerful drive flew over the bar this time.
The pressure from Graham Potter's side was all in vain, as Manchester City added to their lead in the 57th minute.
Young Argentine striker Julian Alvarez sent a fantastic ball over the top to Mahrez, who cut inside before drilling at Mendy's goal.
The Senegalese stopper denied the former Leicester City attacker, but Alvarez was in the right place to tap home his seventh goal of the season.
Raheem Sterling received a good reception from the Etihad faithful when he came on in the 68th minute.
Kai Havertz summed up how things have been going for himself and Chelsea lately as he dragged a tame effort past Ortega's goal in the 77th minute.
Somehow Potter's men didn't score in the 88th minute when a City defender headed the ball on the post.
Sterling then smashed straight at Ortega before Kai Havertz had the ball in the net but was offside.
Nevertheless, Manchester City held on and secured their place in the fourth round of the Carabao Cup.
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Who do Manchester City and Chelsea face next?
Both sides have one game remaining before the 2022 FIFA World Cup, and they will be eager to reach the tournament break with victories in the league.
Next up for Manchester City is the visit of Brentford in the Premier League on Saturday, 12 November.
Guardiola's side are chasing league leaders Arsenal, trailing the Gunners by two points.
Manchester City are unbeaten in their last five games across competitions, winning four and drawing one.
Meanwhile, Chelsea face a tricky trip to St James' Park to face Newcastle United on Saturday.
The Blues sit seventh in the league and have lost two consecutive games with a 4-1 defeat away at Brighton & Hove Albion and a 1-0 defeat at home to Arsenal.
They have now lost three and one two of their last four fixtures.