The first chance arrived for the home team, albeit in a neutral venue at the Puskas Arena, as Dani Olmo’s low header bounced out off the post. Liverpool replied in kind though, Mohamed Salah twice having decent openings, the best of which saw him flick a shot goalwards - saved by former Reds goalkeeper Peter Gulacsi’s shoulder.
Andy Robertson was the improbable player with the most spectacular chance of the first half - a 40-yard shot which caught Gulacsi off his line, having come out of his box to clear a through pass, but which dropped just over the bar onto the roof of the net as the game remained goalless at the break.
That all changed before the hour mark, as Salah latched onto a loose ball from Marcel Sabitzer to bury the opener, before Amadou Haidara misjudged a bouncing ball and allowed Sadio Mane to run in and net the second five minutes later.
Here are five things we learned from the first leg in Hungary.
There were similarities between the first half here and the Reds’ first half against Leicester - but this was arguably even better, with a couple of clearer chances created and certainly more high pressure on the ball in evidence.
They were the better side, the dominant and mostly controlling side, in that first period - albeit without scoring themselves and acknowledging that Leipzig also had their chances.
But, importantly, Liverpool had a clinical touch about them this time: two quickfire goals after the break to capitalise on sloppy play from the Germans.
So many of Julian Nagelsmann’s team’s problems were caused by their own sloppiness in possession.
Dayot Upamecano made headlines this week for his impending transfer to Bayern Munich, but this match served a reminder that he’s far from the finished article - he was very loose on the ball several times, was pressed into errors several times and was certainly nowhere nearby when Salah and Mane ran through on goal.
They didn’t cope well with being pressed high upfield, were overrun with frequency in midfield and didn’t have the physicality to hold off Liverpool’s central men on the turn, meaning it was often Curtis Jones able to change the direction of play and set the Reds onto the attack.
Salah’s super season
His composed finish after the break was a 24th goal of the season for Mohamed Salah - already more goals than he managed last season.
Considering he is also the league’s top scorer domestically and has now netted seven in his last seven games, it speaks volumes for his consistency and quality given the team as a whole have been struggling.
Salah led the press with regularity, tracked back down the wing and made clearances late on - and, most importantly, kept making the runs off the ball in attack.
Once or twice he didn’t get the ball, more times he didn’t get the shot away or missed his chance, but eventually he got his rewards.
Salah and Mane might have been among the goals, but there were two others who produced big showings on the night for the Reds.
At right-back Trent Alexander-Arnold has had a really tough season, well below his best, but here he was excellent defensively for the most part and played a big role going forward, playing early passes, delivering from deep and always in support of Salah.
In the middle, Curtis Jones was arguably the stand-out of the game.
His ball retention, ability to regain possession and non-stop work rate was integral to the Reds’ game plan and he barely put a foot wrong all night.
Second leg and the derby
There couldn’t have been a much better game for Liverpool to return to form and confidence in - if it wasn’t going to happen a month ago, obviously.
The league title is gone now, that much is clear, but there’s still plenty to fight for in Europe if they can find consistency and fortune.
A positive result could act as a reset here and, with the Merseyside derby coming up at the weekend which is a huge match for the top-four race, it’s a much-needed one.
The Champions League is the focus now, but that means both playing in it this season and making sure they’ll be in it next term, too.
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