Having established a 3-1 lead in Lisbon, Liverpool extended their advantage with Ibrahima Konate's powerful 21st-minute header from a Kostas Tsimikas corner.
Benfica equalised through Goncalo Ramos' excellent turn and finish, before Roberto Firmino's two second-half goals - a tap-in followed by a volley - in front of the Kop looked to have put the Reds in control.
But after Roman Yaremchuk broke through to beat Alisson and make it 3-2 on the night, Darwin Nunez scored a late equaliser.
Nunez was then denied by Alisson as Benfica finished strongly but Liverpool held out to advance 6-4 on aggregate.
They now host Villarreal - the club they beat in the semi-finals of the Europa League in 2016 - on 27 April before travelling to Spain for the second leg on 4 May.