Second-half goals from Mohamed Salah and Sadio Mane eased Liverpool into the quarterfinals of the Champions League with a 2-0 second-leg win over RB Leipzig on Wednesday, to complete a comfortable 4-0 aggregate victory.
Liverpool, leading 2-0 from the first-leg yet struggling in the Premier League after six straight home defeats, had several chances to extend their advantage in the first half but lacked sharpness in front of goal.
Both legs of the last-16 tie were played at the Puskas Arena in the Hungarian capital due to Germany's COVID-19 related travel restrictions.
While it was an unusual "home" game for Liverpool, there was a more familiar look to the 2019 Champions League winners' lineup with Brazilian Fabinho back in a midfield role.
Mane had an early chance but blasted over from a promising position yet Leipzig knew one goal for them could set the nerves jangling for Jurgen Klopp's side.
Gulacsi, a former Liverpool player, then did well again to keep out a Salah shot after the Egyptian had been set free by a long ball forward from Thiago Alcantara.
The Germans continued to ask questions though with Emil Forsberg shooting wide from inside the box in the 33rd minute but Liverpool should have had the lead before the break.
Gulacsi parried another Jota effort and then on the stroke of halftime the Portuguese forward wasted a great chance when the ball fell to him at the back post, after poor defending from Dayot Upamecano, but he fired into the side netting.
Liverpool finally broke through in the 70th minute when Jota fed Salah, who cut across the top of the penalty area before drilling into the bottom corner.
Four minutes later, Mane made it 2-0 on the night when he met a Divock Origi cross from the right with a first-time finish, steering the ball home with the outside of his foot.
With the Merseyside club languishing in eighth spot in the Premier League, seven points behind fourth-placed Chelsea, winning the Champions League appears their best shot at qualifying for Europe's elite club competition next season.
"The only reason you play in this competition is because you want to win it," Klopp said.
"I am not silly, we know so far this is not a season which looks like we will win the Champions League, but that doesn't mean we don't want to go as far as possible and then we will see what is possible for us.
"Now we have to wait for the draw; it will be extremely tough whoever we get, but we don't really think that far, we don't have to."
"The two centre-halves played an incredible game. The whole last line played an incredible game because that is a tough task against Leipzig with the runs they make from everywhere," he said.
"We had to press them, force them to play those slightly uncontrolled balls forward. We defended deep together really well which is important. Everybody had a really good game. It was a good performance."