Inter Milan s Croatian midfielder Ivan Perisic (R) vies with Liverpool s Egyptian midfielder Mohamed Salah (L) during the UEFA Champions League round of 16 second leg football match between Liverpool and Inter Milan at Anfield in Liverpool, north west England on March 8, 2022 (AFP)
The Italian champions were unable to scale the mountain they had to climb after losing the first leg 2-0 at home three weeks ago despite Lautaro Martinez's sensational strike into the top corner just after the hour mark.
Alexis Sanchez's red card shortly afterwards punctured any Inter momentum and Liverpool comfortably held out with the extra man to take their place in the last eight.
Inter were left to rue conceding two late goals in Milan three weeks ago after they had enjoyed the better of the game for much of the first leg.
The Italian champions started with a thirst to make amends as they pinned the Reds back in the first half without seriously testing Alisson Becker bar a dangerous Hakan Calhanoglu free-kick that the Brazilian parried to safety.
Liverpool took half an hour to pose any sort of threat, but when they did, they again exposed a frailty in the Inter defence from set-pieces.
Roberto Firmino's header from a corner broke the deadlock when the sides met at the San Siro.
Joel Matip was inches away from a repeat as his header crashed off the bar before, from the resulting corner, Virgil Van Dijk's goalbound effort was deflected wide.
After a subdued first 45 minutes, Liverpool were fired up by Jurgen Klopp at the break and should have taken the lead on the night minutes after the restart when Mohamed Salah turned a loose ball inside the box onto the post.
At the other end, Martinez looked to have wasted the chance to get Inter back in the tie when he dragged a shot wide from the edge of the area.
But the Argentine made amends in spectacular fashion when he arrowed an effort into the top corner from outside the box on 62 minutes.
Inter's joy lasted barely a minute before they were reduced to 10 men by Sanchez's ill-discipline.
The Chilean had been lucky to escape with just a yellow card for a dangerous lunge on Thiago Alcantara just before half-time and stupidly dived in on Fabinho to earn a second yellow.
Salah hit the post again 15 minutes from time and only an incredible block from Arturo Vidal denied Luis Diaz in stoppage time as Liverpool failed to make their numerical advantage count.
Klopp's men failed to score for only the fourth time this season and fell to only a third defeat in 44 games in all competitions.
But their quest for a historic quadruple of trophies remains intact as Inter's 10-men could barely get a foot on the ball in the closing stages, let alone muster another goal to take the game to extra time.
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