However, City had to dig deep after the break in the fact of a fiery Atletico onslaught as the hosts stepped up the pressure.
City though held firm and showed our composure, while Atletico were reduced to 10-men late on when Felipe was shown a second yellow card.
Ederson also produced two stunning saves deep into injury time as we deservedly progressed through to a last four meeting with Real Madrid 1-0 on aggregate thanks to last week’s first leg triumph at the Etihad.
In front of a packed and boisterous atmosphere at the Wanda Metropolitano Stadium, the technical quality of the football more than lived up to the stellar occasion with the game played at a ferocious pace.
It was also a physical encounter with Felipe fortunate to escape an early booking after the Atletico defender clattered into the back of Phil Foden.
It caused an injury that saw the England forward require lengthy treatment and forced to don a head bandage.
Felipe did soon go into the book after another late challenge on De Bruyne with City dominating territory and possession.
All that was missing was a goal and it so nearly arrived on the half hour after a remarkable passage of play.
Gundogan’s follow up header hit Felipe before the hosts frantically cleared the danger.
Ederson was called into action to gather a low deflected Kondogbia drive but City were the dominant side with only the end product absent in a controlled first 45 minutes.
The hosts sought to adopt a more attacking mindset as the second half got underway, and City were grateful to see a Joao Felix header miss the target after the Madrid man gained half a yard on Walker.
Antoine Griezmann then let fly with an instinctive volley which just dipped the wrong side of the post
It was a test of composure with Atleti substitute de Paul almost making an instant impact as his 70th minute effort curled dangerously close.
With the tension at fever pitch then Stones produced a magnificent 86th minute clock to deny Cunha after his shot looked goal bound from Correa’s assist.
City substitute Nathan Ake needed all his wits around him as he calmly cleared in the centre of the box with Luis Suarez waiting to pounce.
The game then boiled over with nine minutes of injury time played, with Felipe shown a second yellow card after a poor follow through on Foden before Stefan Savic received a yellow for following through as Foden nursed an injury.
City though stayed cool, calm and composed with Oblak producing a fine injury time save to deny Gundogan.
Ederson then showed his bravery to produce superb saves from Llorente’s free-kick and Correa's late drive as we earned the ultimate reward of a place in the Champions League semi-finals.
Centre of attention
On a night where every City player stood tall and proud, John Stones epitomised our display with a performance rich in bravery and composure.
His crucial late block to deny an almost certain Atletico goal summed up his display.
Tonight's result meant City boss Pep Guardiola has reached his ninth semi-final, the most of any manager in the history of the competition (four with Barcelona, three with Bayern Munich, two with City).
It also means that City are still to concede a goal in the knockout stages of this season's Champions League.
The only frustration for City was a late yellow card for Joao Cancelo which means he will be suspended for the first leg of the semi-final.
Atletico: Oblak, Lorente, Savic, Felipe, Mandava, Lodi dos Santos (de Paul 68), Koke (Correa 68), Kondogbia, Lemar (Cunha 81), Felix (Suarez 80), Griezmann (Carrasco 68)
Subs: Lecomte, Suárez, Wass, Santos Carneiro Da Cunha, Carrasco, Hermoso, Vrsaljko, Serrano Martínez
City: Ederson, Walker (Ake 71), Stones, Laporte, Cancelo, Rodrigo, Bernardo (Fernandinho 79), Gundogan ©, Mahrez, De Bruyne (Sterling 65), Foden
Subs: Steffen, Carson, Dias, Zinchenko, Grealish, Delap, Edozie, McAtee, Lavia
What it means
City’s reward is a second successive UEFA Champions League semi-final berth – and a mouth-watering last four date against Real Madrid.
We will face Carlo Ancelotti’s men later this month with the first leg at the Etihad set for Tuesday, April 26 with the decider taking place at the Bernabeu on Wednesday, May 4.
Precise dates are yet to be confirmed.
Pep Guardiola reaction
"Today we celebrate because it is the third time in Manchester City's history we are in the Champions League semi-finals.
"It is the champions of Spain and they played with energy and in second half were better than us and we were lucky we didn't concede.
"In the first half we had chances, overall we are in the semi-finals - it is well deserved.
"The opponent is so tough, all the teams in Champions League come here an suffer so it is important we go through."
The big games keep on coming for City as we now prepare for Saturday’s FA Cup semi-final with Liverpool.
It will be the second time we lock horns with Jurgen Klopp’s side in six days following last Sunday’s enthralling 2-2 Premier League draw.
Kick-off at Wembley is 3.30pm with prize on offer for the victors a place in the FA Cup final against either Chelsea or Crystal Palace who will meet in Sunday’s semi-final.
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