The reason why the UEFA Champions League is considered the best club competition in the world is that, besides for being the commercially biggest and richest tournament in the sport, it has a long lineage that creates a level of prestige that can't be denied.

This means that a lot of teams play up to the billing and put their best foot forward in order to make an impact. Every year there's an underdog such as Porto this season or Olympique Lyon last year who usually can be described as "fine" or "solid" but become genuinely dangerous when playing in Europe.

The reason why this has to be stressed is no team has displayed a gap in domestic and European quality quite like this season's Liverpool. In the Premier League, last season's winners have slumped to eighth place and are on a historically bad run of form at home: They've lost six on the bounce at Anfield, a stadium that's always been considered a fortress.

Red Bull (RB) Leipzig and manager Julian Nagelsmann would have relished tackling a famous team at their lowest ebb and yet none of that – the goal drought, the mounting injuries, the visible fatigue – seems to apply on a Champions League night.

For the entire first half, RB Leipzig couldn't catch a break against a defense that Chelsea repeatedly burst through and bottom-of-the-table teams Burnley and Fulham outsmarted. Not because the German side was bad, because Liverpool were legitimately great.

Nagelsmann, known for his tactical precision, used his trademark 3-1-4-2 formation to create an attacking hexagon around the front two of Yussuf Poulsen and Emil Forsberg. The makeshift Liverpool back four of Andrew Robertson, Ozan Kabak, Nathaniel Philip and Trent Alexander-Arnold broke up this formation repeatedly.

Without Poulsen or Forsberg able to get forward into the Liverpool box, Leipzig were reduced to having six players congesting one end of the pitch, leaving plenty of space for gegenpressing down the other.

This was probably intentional from Nagelsmann as Liverpool have been slow and clumsy all season long – but not last night. At the Puskas Arena in Budapest, Hungary, the Liverpool of old were back.

The front three of Mo Salah, Sadio Mane and newcomer Diogo Jota stepping in for the injured Roberto Firmino were electric. In England, they look leggy and can barely string basic one-twos together; in Europe they were outrunning the Leipzig midfield and repeatedly found each other with ease.

If it wasn't for nimble goalkeeper Peter Gulacsi and the ability of Nordi Mukele and Lukas Klostermann to scramble, Liverpool would have run away with it early. Already with a 2-0 advantage, they could have defended all game, instead they wanted goals.

Persistence paid off. Liverpool countered down the pitch and, in the 70th minute, Salah received a short cross from Jota, danced through the Leipzig defense and slotted it in to the bottom right corner. Only four minutes later, his strike partner Mane got one of his own; again on the counter, Divock Origi found a gap in the Leipzig defense on the far right, darted through and made a pinpoint cross to the middle to meet the galloping Mane.

These are textbook goals that both Salah and Mane used to score week in, week out. After such a long drought, they're a rare treat.

Liverpool won 2-0, 4-0 overall, with two genuinely remarkable performances and progress into the quarterfinals. If it can be said that teams play their best in Europe, Liverpool took that to a whole new level and turned into a completely different team.