Liverpool eased past RB Leipzig in to the Champions League quarter-finals with a 2-0 win in Budapest Wednesday thanks to two second-half goals to provide the Reds a 4-0 aggregate win.
Repeating their double brace from the first-leg Mohamed Salah and Sadio Mane struck within four minutes to settle the tie and keep alive Liverpool's hopes of rescuing their season with European glory.
After six successive defeats at Anfield, Jurgen Klopp's team looked relieved to be abroad, with the next leg also played in Hungary because of Covid-19 travel restrictions.
But as the Reds showed attacking intent from the off, they squandered a string of chances throughout the first-half.
Unmarked at a corner, Diogo Jota must have opened their account in the 18th minute but the Portuguese striker directed his header straight at Hungarian goalkeeper Peter Gulacsi who tipped over.
Midway through the time an acrobatic scissors kick by Thiago Alcantara released Salah but his left-footed effort was blocked by Gulacsi with Mane unable to convert the rebound.
On the half-hour the onrushing Salah couldn't finish from close-range a cross by Trent Alexander-Arnold who was simply sent clear on the proper with a slide-rule go by Mane.
Roused at last by the near misses, the German side started to venture beyond Liverpool's high line and managed to carve out some chances of their own.
On the half hour Kevin Kampl forced a save from Alisson Becker with a curler from distance, while a minute later Swedish playmaker Emil Forsberg, back from injury, clipped a snapshot just wide of the post.
Still the better chances were Liverpool's with Jota again firing straight at Gulacsi just before the break and in to the side-netting on the whistle after a slip by French defender Dayot Upamecano.
Leipzig, flying domestically on the trunk of six straight Bundesliga wins but nervy in Budapest, urgently needed an objective to rattle Liverpool but continued to lack penetration in the second half.
In reality, Julian Nagelsmann's men, who dumped Tottenham out at this stage of the competition last year and Manchester United in the group stage this season, rarely looked like claiming a straight bigger scalp by turning the tie around.
Their last opportunity arrived on 65 minutes but Alexander Sorloth's header from a cross by Hee-Chan Hwang spun over Alisson's fingertips only to rebound out from the bar.
Immediately after Salah and Mane ruthlessly punished the let-off by securing Liverpool's berth in the last eight.
In the 70th minute the Egyptian fired an area past Gulacsi, then four minutes later Mane turned a cross by substitute Divock Origi past the hapless Hungarian.