And, despite a shaky start to their campaign in the group phase, Liverpool remain on course for a third final in four seasons.
Liverpool boss Rafael Benitez paired Martin Skrtel with Sami Hyypia in central defence - pushing Jamie Carragher out to right-back - and they were tested in a closely-fought first half.
Reina was outstanding as Liverpool defended their two-goal advantage from the first leg, and he was in action after eight minutes as he dived low to his right to save from Cruz.
Liverpool threatened to open up the Inter rearguard for a crucial away goal after 24 minutes when Fabio Aurelio's long ball almost released Ryan Babel, but keeper Julio Cesar was swiftly off his line.
The visitors were by no means sitting on their lead, and a slip by Esteban Cambiasso let in Torres and Cesar needed to be alert at his near post to block the Spanish striker.
Inter's best chance came after 29 minutes when Zlatan Ibrahimovic played in Cruz, but he pulled his finish across the face of goal.
Reina did well again on the stroke of half-time when Cruz met Maicon's cross with a neat flick, but Liverpool's keeper was again quick to react and keep his side level.
Inter's hopes of mounting a fightback were dealt a cruel blow after 49 minutes when Burdisso - who had already been booked - collided with Lucas.
The challenge looked innocuous and Inter were understandably enraged when Norwegian referee Tom Henning Ovrebo produced a red card that was harsh in the extreme.
It was a stroke of luck for Liverpool and ill-fortune for Inter, who saw Marco Materazzi sent off in debatable fashion in the first leg at Anfield.
Ibrahimovic once again flattered to deceive and was guilty of an awful miss after 56 minutes when he was gifted the ball by a dreadful pass from Skrtel and was wastefully off target.
And Torres made Inter pay for all those missed opportunities as he fired the goal that effectively sent Liverpool into the last eight after 64 minutes.
Aurelio's pass found Torres in the area and he turned before sending a low, unerring right-foot finish low to the right of Inter keeper Cesar.
Liverpool were now cruising, although there was another opportunity for Ibrahimovic to incur the wrath of the home crowd with another bad miss after 78 minutes, shooting horribly off target again when clean through.
Inter Milan: Julio Cesar, Maicon, Burdisso, Rivas, Chivu, Zanetti, Cambiasso, Stankovic (Jimenez 84), Vieira (Pele 76), Ibrahimovic (Suazo 80), Cruz. Subs Not Used: Toldo, Figo, Crespo, Maniche.
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