Trailing 3-0 from the first leg, City’s Gabriel Jesus scored after 116 seconds following Raheem Sterling’s pass.
Liverpool reached their first Champions League semi-final for 10 years after coming from behind to win at Manchester City and secure a 5-1 aggregate win.
Bernardo Silva hit the post before Leroy Sane had a goal disallowed for offside despite James Milner getting the last touch. Mohamed Salah equalised on the night before Roberto Firmino hit the winner.
Liverpool will discover their semi-final opponents when the draw is made on Friday [12:00 BST] in Nyon, Switzerland. City manager Pep Guardiola was forced to watch the whole of the second half from the stand after being sent off by Spanish referee Antonio Mateu Lahoz at the end of a controversial first half.
In a breathless opening 45 minutes City dominated and peppered the Liverpool net with 14 shots. The visitors did not have a shot on target until the 41st minute but were much improved after the break.
Salah’s 39th goal of the season, a smart finish after Sadio Mane had gone to ground inside the City penalty area, left the hosts needing four goals. Firmino earned Liverpool their third win over City this season after a mistake by Nicolas Otamendi.
Source: BBC News