Liverpool goal-scorers Mohamed Salah and Roberto Firmino celebrate the opening strike by Salah against Manchester City. Photo: Rui Vieira/AP

Liverpool survived a first-half bombardment, and benefited from a controversial offside decision, as they beat Manchester City 2-1 in their Champions League quarter-final second leg on Tuesday to win the tie 5-1.

Gabriel Jesus gave City a second-minute lead at the Etihad Stadium, raising hopes of a stunning comeback after they lost 3-0 in last week's first leg.

But City’s Leroy Sane had a goal wrongly disallowed for offside just before the break, and Mohamed Salah and Roberto Firmino both netted after the break for Liverpool.

Meanwhile, Kostas Manolas capped a sensational Roma comeback as the Italian side shocked Barcelona 3-0 in Tuesday’s Champions League quarter-final second leg to progress on away goals, after the tie finished 4-4 on aggregate.

Edin Dzeko’s early goal at the Stadio Olimpico gave Roma hope of overturning a 4-1 deficit from the first leg, before Daniele de Rossi converted a 58th-minute penalty.

Greece international Manolas completed an improbable turnaround eight minutes from time by glancing in a header from a corner.