Aguero's heavy tackle on David Luiz sparked the stoppage time melee as both sets of players clashed, with Fernandinho also shown red for grabbing Cesc Fabregas by the neck and forcing him off the pitch.
Argentina's Aguero can expect a four-game ban for violent conduct as this is his second such suspension of the season, missing key matches over the festive period.
Manager Pep Guardiola issued a post-match apology for the incidents.
"It's a pity it finished like this. I don't like that. I apologize for what happened," he said.
For Antonio Conte's Chelsea it was an eighth straight EPL win, ensuring the west London side would top the standings for another week, four points clear of City,
Chelsea trailed to a goal on the stroke of halftime as Gary Cahill deflected a cross by Jesus Navas cross past his goalkeeper Thibaut Courtois.
City might have been further ahead on the hour mark when Kevin De Bruyne crashed a Navas cross against the bar from close range.
Chelsea took full advantage and EPL top scorer Diego Costa leveled on the hour after fending off Nicolas Otamendi from a Cesc Fabregas pass.
Chelsea was ahead 10 minutes later as substitute Willian burst clear to beat City keeper Claudio Bravo with some aplomb.
Eden Hazard rounded off the scoring, outpacing Aleksandar Kolarov to wrap up the three points.
Then came the late clashes, with Luiz left with a large ice pack on his left knee as a result of the Aguero challenge.
"I don't like to speak about these type of things. Aguero is an amazing player who does a lot for football," he told Sky Sports.
"We showed our power. It also shows our character that we didn't lose our heads," he added.
Before the match there was a minute's silence as a mark of respect to those who lost their lives in the Colombian plane crash earlier this week.
Luiz, also paid tribute to the Chapecoense team hit by the tragedy. "I prefer to give this victory to the people that died in Brazil.
"It's been a difficult week for everyone. We need to pray for the families," he added.
Later Saturday, both Arsenal and Tottenham Hotspur kept pace in an open title race with emphatic five-goal victories.
Harry Kane and Christian Eriksen scored doubles as Spurs thrashed bottom club Swansea 5-0 at White Hart Lane.
North London rival Arsenal won a one-sided derby match at West Ham 5-1, with Alexis Sanchez scoring a second half hat-trick.
The win lifts Arsene Wenger's men to second in the standings, three points adrift of Chelsea.
Liverpool missed the chance to close to within a point at the top when it threw away a 3-1 lead at Bournemouth Sunday to lose 4-3 in a stunning upset.
Goals from Sadio Mane, Divock Origi and Emre Can against a penalty for Callum Wilson left Jurgen Klopp's team in charge until late drama.
Ryan Fraser pulled one back then Steve Cook drew the Cherries level.
Not content with a point, the home side took full advantage when Liverpool goalkeeper Loris Karius could not hold Cook's shot and Nathan Ake scored the 93rd minute winner.