Liverpool took charge of ita Champions League last-16 tie against RB Leipzig with a 2-0 win in the first leg in Budapest.
Julian Nagelsmann's side, which pipped Manchester United to a place in the knockouts, looked far from comfortable in the unfamiliar surroundings of the Puskas Arena, where the game was held to due to coronavirus travel restrictions.
Mohamed Salah's 24th goal of the season put Liverpool ahead after a mistake by Kevin Kampl, and Sadio Mane doubled the advantage when Nordi Mukiele gifted him an opportunity.
The Reds are unbeaten in six away games against Bundesliga opposition stretching back to 2002, and Jurgen Klopp's men will be firm favourites to progress to the quarter-finals.
Liverpool nearly fell behind after just five minutes, Dani Olmo's diving header hitting the inside of the post from Angelino's cross.
The away side looked the most threatening as it began to take control, and Peter Gulacsi was alert to block a Salah effort from close range before Roberto Firmino fired a shot into the side-netting.
Mane then headed over from six yards from a Firmino cross, and the Senegalese thought he had set up his strike partner to nod in the opener after errors from Dayot Upamecano, but the ball had gone out of play.
Christopher Nkunku had barely been involved in the first half but he could have given Leipzig the lead early in the second, Alisson saving well after the striker ran onto Olmo's through-ball.
It was Salah who broke the deadlock 53 minutes in, drilling past Gulacsi after a dreadful backpass from Kampl, and it soon got worse for Leipzig.
Mukiele made a complete mess of a simple clearance forward by Curtis Jones, and Mane had time to stride into the box and slot home.
Angelino had a chance to pull a goal back but sliced his attempt badly, summing up a poor game for last season's semi-finalist.