When Benfica chased the equalizer, Liverpool's goalkeeper Allison offered entertainment and dribbled as the last man away Rafa Silva in a daring maneuver.
In the final minutes, Luis Diaz came in a quick change, got help from Benficafot, and rounded the goalkeeper Odisseas Vlachodimos and put in 3-1 and decided the match.
It was only two minutes after Alisson's effort.
Mighty song by Liverpool fans filled Estádio da Luz where almost 60,000 sat down.
It hailed bottles and other objects at the former Porto player Diaz after his goal.
Benfica were on for an equalizer at 1-2 and were close several times.
With 67 minutes played, Darwin Nunez of Virgil van Dijk fell dramatically just outside the penalty area.
The striker called for a penalty, but was not heard from referee Jesús Gil Manzano because the filming was too obvious.
Liverpool won their fifth away match in a row in the Champions League, which is a club record.
City only got 1-0 against Atletico
In Tuesday's second quarter final, Manchester City faced Atletico Madrid.
A City that had 17 straight Champions League matches at home without a loss.
The home team dominated the match as expected and had a ball possession of 70 percent, but despite that City did not manage to create a really dangerous goal chance.
But in the 70th minute of the match, Phil Foden had the chance to free-kick Kevin De Bruyne who put 1-0 in the far post - which was also the end result.
Now thriller matches await next week on Wednesday.