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Late goals from Roberto Firmino and Mohamed Salah in last month's first leg ensured the Reds were in control of the tie heading into the return fixture.
The host hit the frame of the goal through Joel Matip and Salah and looked under no threat until the point Lautaro Martinez fired in a stunning goal for Inter with an hour played.
Alexis Sanchez was sent off 107 seconds later for a second yellow card, however, and it was Liverpool who went closest to scoring the next goal when Salah struck the post.
Thiago Alcantara and Matip returned to Liverpool's line-up and the latter picked out the crossbar from the best of Liverpool's limited first-half openings.
Milan Skriniar superbly blocked Virgil van Dijk's goal-bound header moments later, while Hakan Calhanoglu tested Alisson at the other end from a low free-kick.
Liverpool slowly started to turn the screw and should have been out of sight in the tie, only for Salah to fire against the upright after Diogo Jota was denied by Samir Handanovic.
Those wasted chances came back to haunt Jurgen Klopp's side when Martinez unleashed a swerving 20-yard shot into the top-right corner.
Sanchez, who received a yellow for a challenge on Thiago late in the first half, was sent off for following through on the same opponent almost immediately after Martinez's goal.
Liverpool was further frustrated as Salah's cushioned volley came back off the upright, but the host protected its one-goal aggregate lead to reach the last eight.
