Trailing 3-0 from the first-leg City manager Pep Guardiola had said his team needed to produce a “perfect game” at the Etihad Stadium if they were to achieve a famous comeback and for 45 minutes they were not far off that level.
Yet it was Liverpool whose approach turned out to be perfect in the circumstances as they followed up some staunch first-half defending to level through Salah in the 56th minute and seal the tie through Firmino 13 minutes from fulltime, clinching their third win against City this season.
Gabriel Jesus had scored for the hosts after two minutes to fuel the home fans with hope and Guardiola's side had then launched wave after wave of attacks to pin Liverpool back.
Yet after Bernardo Silva hit the post in the 40th minute and Leroy Sane had an effort ruled out for a disputed offside two minutes later, City had just the solitary goal to show for their first-half exertions.
After a glorious attacking display in the first leg, Liverpool did exactly what they had to do in Manchester and deservedly took their place in the semi-finals.