The Egyptian netted his 25th goal of the season to open the scoring in the Budapest affair and Sadio Mane then quickly followed with a close-range finish.
Extended highlights: LFC 2-0 RB Leipzig
Those goals made it 4-0 on aggregate in the last-16 tie, providing a much-needed boost for the Reds after a testing period.
Read on for BT Sport's post-match interview with Salah…
On the result...
It's a big result for us. We lost a few games in the Premier League and the team is not in the best shape, but we want to fight in the Champions League and we will also fight in each game in the Premier League and we will see what will happen.
On a controlled and positive performance...
It's really positive. To be fair, it's a tough team, they play football, they make us run a lot today and we try to play our way, press high and get the ball and counter-attack. I think we did well, we won the game – that's the most important thing. It's positive to take from that game and hopefully we can keep continuing with that in the Premier League as well.
On missing a few chances in the first half and potentially getting nervous...
I scored with numbers this season and I would love to score more, but it's part of the game that you miss chances. You want to score all the time, you want to help the team but as long as the team keeps winning, that's the most important thing. I'm happy to score the first goal today and that the team won. That's the most important thing.
On the backline...
I think it's hard, we had a few players that got injured – Virg, Joe, Joel, then Hendo. We tried to play Hendo at centre-back and Fabinho from midfield to centre-back, so you lose Fabinho in the midfield. We had a few injuries this season, we were unlucky, but the most important thing is that we keep fighting. I know it's really hard and everybody can see that but as [long] as everybody tries to give 100 per cent and keeps fighting in the game, I think we just need to take each game at a time and just focus on the next game. We don't have to look at the big picture because sometimes when we look at the big picture, we get pressure and too much pressure we can carry on the pitch. But we just need to leave the pressure off the field and just play football.
On whether Liverpool approach the Champions League with a different mindset because it's away from the Premier League...
It's been tough in the Premier League, everybody can see that. We don't want it to be tough but it's a part of the game. The last couple of years we were winning, we were flying. This year, we had a few injuries, so we were unlucky. You have young players and they are really playing good but sometimes you struggle to put someone in centre-back. But now we have two centre-backs or three or four – hopefully now we can keep winning.