Liverpool capitalised from one of a number of errors from Dayot Upamecano to take a 2-0 first leg away lead over RB Leipzig in the Champions League round of 16 thanks to goals from Mohamed Salah and Sadio Mane in Budapest on Tuesday.
The match was moved to neutral Budapest as the rising coronavirus cases in the UK had prevented Liverpool from entering Germany.
And perhaps the unfamiliar surroundings troubled Leipzig as Liverpool started far better and were unlucky not to be ahead before half-time.
Jurgen Klopp's side have been in terrible form domestically with three consecutive defeats in the Premier League but took a deserved lead on 53 minutes.
"It was the game we wanted, the game we needed," Klopp told reporters. "Leipzig can be a real monster, they overrun teams, they are really physical and tonight we controlled them in an exceptional way. We forced them to make mistakes. I am happy with the performance."
Leipzig centre-back Upamecano, who it was recently announced would join Bundesliga rivals Bayern Munich in the summer, had been guilty of some erratic passing in the first half and was caught out of position as Salah snuck in behind the defence to slot past goalkeeper Peter Gulacsi.
Upamecano was at fault for the second goal five minutes later after a woefully timed challenge allowed Mane to run through and put Liverpool 2-0 ahead.
The return leg is due to take place at Anfield on March 10, though that situation is under constant review due to the ongoing coronavirus situation in the UK.
"It was an important game for us, a tough game," Liverpool captain Jordan Henderson said. "Keeping a clean sheet was important for us.
"We just want to keep going and keep fighting every time we play. There have been a lot of difficult situations throughout the season, but we've just got to take each game as it comes and take things one step at a time.
"A good win but it's only half the job done," he added.
The Germans, who came into the match on a four-game winning run in all competitions, were largely toothless in attack following the goals until Tyler Adam's miss in stoppage time.
"In the return leg we have to pick up where we left off. Then we will have chances," Marcel Sabitzer said, adding that Leipzig had played a good game apart from the two errors.
"We played a really good game and we got the result we deserved," Klopp added. "We defended really well and had good recovery. It was a tough game with only two days since the last one. "It's only the first leg, we know that but a lot of people were waiting for us to slip again," the German added.
"For two years we were really good and this year we have problems, that's fine. A lot of people expected us to slip again but the boys didn't."