The Reds were eager to avoid a City backlash after a 3-0 first-leg win, despite missing influential midfielder Jordan Henderson.
However, there was a welcome boost ahead of kickoff with Mohamed Salah passing a late fitness test and drafted into the side immediately, while the Citizens pulled their tried and tested in a back-three formation.
The home side got the start they wanted with a second-minute lead after Gabriel Jesus latched onto a Raheem Sterling pass to fire into the bottom corner amidst Liverpool remonstrations for a foul on Virgil Van Dijk in the build-up.
The goal eased the pressure on Pep Guardiola’s side as they were able to play passes around with ease, leaving the Reds at sixes and sevens.
Belgian Kevin De Bryne looked to get his name on the score-sheet with two quick-fire efforts, the first a looping header that sailed wide followed by a low tame shot following a corner.
It was all City at this stage as they went close yet again following a shot by Bernardo Silva, which ended up being blocked on its way to goal by James Milner.
City were becoming more threatening and Silva rattled the post with a stinging drive from the right after cutting inside moments before halftime.
Alex Oxlade-Chamberlain, one of the stars of the first-leg, got the visitors first chance after beating a few defenders before hoofing his shot over after rounding Ederson.
At halftime, Guardiola’s backlash at the match officials for his displeasure at the decision-making for disallowing Leroy Sane’s goal saw him sent to the stands.
Liverpool handed themselves a breather after relentless pressure in the first half. Sadio Mane broke through the central defence to set-up Salah for a cool finish in an unguarded net.
The pressure was back on City, who now had to score four goals without reply, while the Merseyside club was more at ease with the away goal to boot.
Despite the Citizens best efforts to get back in the game, Roberto Firmino killed off any prospects of a comeback with his eighth of the competition after latching onto a loose ball before beating his countryman on 76 minutes as Jurgen Klopp’s side march into the last four for the first time since 2007.