Son Heung-min was their hero. The South Korean scored the only goal of the game in the 1-0 first leg victory at the Tottenham Hotspur Stadium on 9 April and on Wednesday night at the Etihad, he bagged a brace to give Spurs a 3-1 aggregate lead.
But City responded through Bernardo Silva, Raheem Sterling and Sergio Aguero. That made it 4-3 to the hosts. However Fernando Llorente had the final say.
His bundled finish in the 76th minute had to be confirmed by the video assistant referee - VAR.
The same technology was deployed in stoppage time when Sterling's goal was ruled out for offside.
“I support VAR but maybe from one angle Fernando Llorente’s goal is handball, maybe from the referee’s angle it is not,” said Manchester City boss Pep Guardiola.
“I am for fair football, for fair decisions,” he added. “The referees must be helped sometimes. When it is offside, it is offside. What can I say?”
His Spurs counterpart, Mauriccio Pochettino, hailed his players' resilience. “I think they are heroes,” he said. “They deserve a lot of praise. To be in the semi-final was a dream before and now we are there.”
Pochettino said he believed Spurs could become the second London club after Chelsea to win the Champions League.
“We showed here in Manchester and last week that all is possible in football.
"Sport always gives you the possibility to beat teams that no one thinks we are capable of beating. Football is not only about talent but belief. This team has the personality and mentality to believe all is possible.
"That is a massive achievement for us. With this belief, we can achieve big things.”
Liverpool, by contast, eased into the last four. Already 2-0 up from the first leg at Anfield, the tie against Porto was effectively finished when Sadio Mané opened the scoring at the Estádio do Dragão.
That strike meant Porto needed to score four goals - a feat no team has achieved against Jurgen Klopp's men this season.
Mohamed Salah made it 2-0 on the night mid way through the second-half before Eder Militao scored for the hosts.
It wasn't even a consolation. Roberto Firmino and Virgil van Dijk added two more to underline the gulf.
“We are in the semi-final against Barcelona," said Klopp. "I’m really happy about the fact we play them. It is really good news that there is a proper football game between Liverpool and Barcelona."
Klopp, whose side lost last year's Champions League final against Real Madrid, added: "To be in the semi-final for a second time in a row is a big statement. I’m really proud of the boys, it is brilliant what they did. Doing it in different ways makes it even more special.”