City held a 1-0 advantage going into the tie at the Wanda Metropolitano Stadium and held on for a goalless draw in a fiery encounter which turned ugly in the final moments.
With the tie slipping away from the hosts, some Atleti players struggled to contain their emotions and bitterly lashed out at their opponent.
In particular, a tackle on Phil Foden sparked a mass brawl in the 89th minute, made worse by the behavior of Atlético defender Stefan Savić who somehow escaped with just a yellow card for what came next.
The defender was furious as Foden rolled around on the pitch after being brought down by Felipe, who saw a second yellow card and was dismissed for the challenge.
Savić ran over and tried to drag Foden off the ground before being stopped by Manchester City's players. He then pulled at City substitute Jack Grealish's hair after the Englishman appeared to call him an expletive amid the melee.
'The fans will be proud'
The drama lit the torch paper around the stadium as the home support created an intimidating atmosphere for the final minutes of the match.
Fans were encouraged by Atleti manager Diego Simeone who also received a yellow card in added time as the hosts appeared to lose all composure.
"I'm proud of what we've been able to do. Our fans were extraordinary, pushing the team on and then responding, in kind, by raising the noise still further once the team were close to winning," Simeone told reporters after the match.
"I've no doubt whatsoever that the fans will be proud of how we compete, that's the key. However you do it, you compete.
"The only thing to emphasize is that we didn't win and that's all that truly counts."
Even at full-time, Savić continued his feud with Grealish down the tunnel as police were needed to separate the two teams at the mouth of the changing rooms.
The ugly scenes ruined what was otherwise a brilliant performance from the Colchoneros who wasted a number of chances to level the tie against a tired looking City.
"In this stadium, in this competition, it is always difficult. It is a big compliment for the players," City manager Pep Guardiola told reporters, not wanting to be drawn into questions about the scuffles.
"We cannot expect every time to make everything marvelous. We have to suffer.
"I am proud because the opponent was really good. We tried to take the ball but were not able."