They will now face the winners of the other semi-final between Chelsea and Real Madrid in Istanbul later this month.
The tie is delicately poised following a 1-1 draw at the Estadio Alfredo Di Stefano last week.
They created enough chances to have clawed back the two-goal deficit but goalkeeper Thibaut Courtois was hardly extended.
City responded in the second half with a penalty from Riyad Mahrez and a fine effort from Phil Foden to win 2-1.
The Black and Yellow were minutes away from claiming a 1-1 draw from the first leg at the Etihad.
Los Blancos travel to Merseyside boasting a 3-1 lead from the first leg in Madrid, where Vinicius Junior bagged a brace.
Madrid’s entire XI in Italy had a paltry three goals in the competition this season between them at kick-off.
The Arsenal forward, who was also flagged offside on four occasions, knows his subpar performance could prove costly.
Chelsea have not been competitive in Europe’s top competition for too long.
PARIS: With no Neymar and Angel Di Maria tonight, coach Mauricio Pochettino feels he will…