A moment of magic from Philippe Coutinho secured a 1-1 draw for Liverpool and a place in the Europa League quarter-finals at the expense of bitter rivals Manchester United.
Jurgen Klopp's team claimed a dominant 2-0 win at Anfield a week ago but United were much improved from that lacklustre showing and sparked hopes of a turnaround when the impressive Anthony Martial won and netted a 32nd-minute penalty.
Visiting striker Daniel Sturridge struck the crossbar before Coutinho extinguished United's ambitions of a comeback with an exquisite solo goal on the stroke of half-time.
Louis van Gaal's team were criticised for their lack of creativity in the opening game - they created chances on this occasion but were regularly wasteful inside the area.
Klopp can now look forward to the last eight and the possibility of an emotional meeting with former club Borussia Dortmund, while Van Gaal will begin his attempts to salvage something from a forgettable United campaign in Sunday's Premier League derby at Manchester City.
Liverpool goalkeeper Simon Mignolet made up for indecision under Marcos Rojo's left-wing cross with a stunning reaction save from Jesse Lingard's header and, by the time Juan Mata dragged a 19th-minute volley wide, United had already shown more attacking threat than they did in the opening leg.
Martial cut in from the left to fire over, while Liverpool were largely operating on the counter-attack - an approach almost rewarded when David De Gea got down superbly to keep Coutinho's drive out of his bottom-left corner.
There was an unfortunate role-reversal for Nathaniel Clyne, who won Liverpool's penalty at Anfield last week.
The England full-back was undone by the quicksilver Martial and brought down his man, who promptly steered home from 12 yards.
Daniel Sturridge curled an angled free-kick against the crossbar and Jordan Henderson blazed over as Liverpool sought an equaliser on the night, but United should have levelled the tie two minutes before half-time.
Marouane Fellaini touched Daley Blind's long ball back across the six-yard box for Rojo to shoot narrowly wide with Mamadou Sakho in close attendance.
It would prove to be a costly miss as Coutinho closed the half in dazzling fashion - shimmying beyond Guillermo Varela and placing a nonchalant chip past De Gea at his near post.
Van Gaal appeared to punish Varela's part in the goal by sending on Antonio Valencia in place of the Uruguayan youngster for the second period.
Michael Carrick was quietly influential and orchestrated a move where Sakho made a last-ditch challenge on Marcus Rashford before the teenage striker skewed wide on the turn.
Fellaini, booked earlier for his regular offence of catching an opponent with a flailing arm, headed straight at Mignolet from Carrick's cross as the game passed the hour.
Sturridge's hacked finish was an ill-fitting companion for the majestic Coutinho dribble that set up the chance and the Liverpool striker was nonplussed when he made way for Divock Origi in the 68th minute.
Martial and Fellaini failed to make Mignolet work with opportunities either side of that change.
United appeared sapped of energy as the clock ticked down and De Gea was at full stretch to deny Coutinho his second goal in a match where the Brazilian's contribution will be long remembered.