There was hope, Jack Grealish scored a few minutes after the break, and Bernardo Silva scored in the 90th minute to ensure a nervous ending.
Tapped from close range.
Liverpool advance to the final where they will face either Chelsea or Crystal Palace who will face off on Sunday. Mane later told the BBC that the day was special.
We were playing one of the best teams in the world. Winning a game like this, especially in the semi-finals, is a big, big, big win." We were so happy to win and qualify for the final
Liverpool defender Conte continued his rich vein of goal-scoring form as he drove a header from his side's opening corner of the game - his third goal in as many games.
The moment was similar to his struggle in the Premier League last week, when regular starter Ederson was also lulled to the ball but was able to smack the ball ahead of the fast-moving attacker.
Surprised by two goals, Manchester City were finally able to gain a foothold in the encounter, as the defending Premier League champions pushed to get back into the game.
England international Jack Grealish finished his spot in the top corner after opening up a shooting opportunity after some clean play from Gabriel Jesus.