City held a 1-0 advantage before the first leg at the Wanda Metropolitano Stadium and held for a goalless draw in a fiery encounter that turned ugly in the final moments.
As the tie slipped away from the hosts, some Atleti players struggled to contain their emotions and savagely slapped their opponents.
In particular, a tackle on Phil Foden in the 89th minute sparked a mass brawl that was made worse by the behavior of Atlético defender Stefan Savić, who somehow only got away with a yellow card for what came next.
The defender was furious as Foden rolled around the pitch after being brought down by Felipe, who saw a second yellow card and was sacked for the challenge.
Savić ran over and tried to pull Foden off the ground before he was stopped by the Manchester City players. He then pulled City substitute Jack Grealish’s hair after the Englishman called him a strongman amid the melee.
“The fans will be proud”
The drama lit the torches around the stadium as the home side created an intimidating atmosphere in the final minutes of the game.
The fans were encouraged by Atletico manager Diego Simeone, who was also booked in added time as the hosts seemed to lose their composure.
“I’m proud of what we’ve accomplished. Our fans have been exceptional, they pushed the team forward and then responded in kind, raising the noise even more when the team was about to win,” said Simeone then told reporters the game.
“I have no doubt the fans will be proud of how we compete, that’s the key. However you do it, you compete.
“The only thing we have to emphasize is that we didn’t win and that’s all that really matters.”
Even full-time, Savić continued his feud with Grealish down the tunnel as police were needed to separate the two teams at the entrance to the dressing rooms.
The ugly scenes ruined an otherwise brilliant performance by the Colchoneros, who missed a number of chances to level the tie against a tired-looking City.
“In this stadium, in this competition, it’s always difficult. It’s a huge compliment for the players,” City manager Pep Guardiola told reporters, who didn’t want to be drawn into questions about the scuffle.
“We can’t expect to make everything wonderful every time. We must suffer.
“I’m proud because the opponents were really good. We tried to take the ball but we couldn’t.”
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Elsewhere, Liverpool played an exciting 3-3 draw with Benfica but won 6-4 on aggregate to advance to the semi-finals.
Ibrahima Konaté scored Liverpool’s first goal of the night before Gonçalo Ramos equalized before half-time.
A brace from Roberto Firmino seemed to end the tie in the second half, but Benfica made things a little more interesting after hitting back twice through Roman Yaremchuk and Darwin Núñez.
But the damage was done in the first leg and Liverpool reached the last four where they will meet Villarreal.
Meanwhile, Manchester City meet 13-time winners Real Madrid for a spot in the final.