Match ends, FC Red Bull Salzburg 0, Liverpool 2.
Liverpool manager Jurgen Klopp said he loved that his side were "so smart" as they beat Red Bull Salzburg 2-0 to reach the Champions League last 16 as Group E winners.
The defending champions, who needed at least a point to progress, were on the ropes at times in the first half against a side who had scored 87 goals in 24 games.
But from the moment Naby Keita headed in Sadio Mane's cross, there was only going to be one winner.
Mohamed Salah clinched victory 100 seconds later with an excellent right-footed finish from a ludicrously tight angle.
"I couldn't have more respect for what Salzburg is doing," said Klopp. "I know how people see it - you think being the best team in Austria is 'OK'.
"Then you see how good they are, how good they were in the first game [the Reds won 4-3 at Anfield], how good they were against Napoli and Genk and then you could come here as the current Champions League winner and misunderstand that situation.
"And I love it, I really love it that my team is so smart that they listen and they put in a shift in like that. Salzburg was unbelievably strong, especially in the first half, but we as well were ready for that fight."
Klopp's side needed the three points to top the group because Napoli beat Genk 4-0.
The Reds will discover their Champions League last-16 opponents in Monday's draw in Nyon, Switzerland (11:00 GMT). Real and Atletico Madrid are both possible opponents.
Salzburg drop into the Europa League last 32. Their 19-year-old striker Erling Braut Haaland had chances to score but failed to become the first player to score in his first six Champions League appearances.
"It was a bit like a heavyweight boxing contest," said Salzburg boss Jesse Marsch. "We fought really hard, but they fought back. In the end they got two more punches in. That's how close the margin is between victory and defeat in the Champions League."
Reds comfortable winners... eventually
Liverpool had hoped to have sealed their last-16 place before the final group game - but they came to Austria needing a point against a side who pushed them all the way in a 4-3 thriller at Anfield.
Salzburg started at an electric pace, with Virgil van Dijk having to stop Haaland from having a one-on-one with Alisson after 15 seconds.
There were nine shots on target before the break - the most in the first half of a Champions League match without there being a goal since Schalke v Manchester United in April 2004.
Alisson needed to make six saves in the first half, although Liverpool arguably had the best chance when Salah shot wide from close range when completely unmarked.
The Egyptian also fired over the bar from eight yards after the restart.
Two shaky moments from Salzburg keeper Cican Stankovic eventually settled the game. He rushed off his line to try to take the ball off Mane, who was able to cross for Keita to head into an empty net - both former Salzburg players.
And less than two minutes later he again left his goal unguarded, with Salah going round him before somehow finding the net with his right foot from a tight angle outside the box - a chance much harder than many of the eight shots he failed to score with.
They never looked back after that and kept a second clean sheet in a row, having conceded in each of the 13 matches before that.
"Jesse and his team worked great with their team and gave them a fantastic attitude; they used what they could use, but we also played very well in the spaces," said Klopp. "When we started to play more intelligently and use the spaces we had in the second half then we used our opportunities.
"We had 21 attempts on goal and we could have scored five or six times, so it was really difficult for Salzburg in the second half. But, once again, my highest respect for Jesse and his team."
End of the party for Salzburg
Salzburg were one of the stories of the group stage, with 16 goals in their opening five games - more than the two teams who finish above them. Only two teams - Bayern Munich and Tottenham in Group B - have scored more.
In fact 19-year-old Haaland, with eight goals, has outscored 17 teams including Barcelona, Borussia Dortmund and Atletico Madrid.
Needing to win, they had chances in a frantic start - which could have seen the game play out very differently - with the lively Hwang Hee-chan and Takumi Minamino having shots saved by Alisson in quick succession.
But only three teams have conceded more goals in the group stages than the 13 Salzburg have let in and their race was run after the two quick-fire Liverpool goals,
Norway striker Haaland was replaced in the second half, having only had three shots and 23 touches - although he has still scored 28 goals in 22 games this season.
The Champions League's loss is the Europa League's gain, with the Austrian champions moving into that tournament. Although Haaland could be back if he joins one of the many Champions League clubs he is being linked with next month.
"We are very disappointed, as we played really good football, and we probably couldn't have played any better than in the first half," said boss Marsch. "At the moment the disappointment is dominating, but in a couple of days we will be very proud."
Match stats - only Messi betters Salah's record
- Liverpool have progressed from all three of their Champions League group stages under Jurgen Klopp. They had been knocked out at this stage in their previous two Champions League campaigns before his arrival.
- Salzburg's 16 goals is the most scored by a side to be eliminated from their Champions League group since Chelsea in 2012-13 (also 16).
- Liverpool kept a clean sheet in an away Champions League game for the first time in 11 matches, having conceded 18 goals in their previous 10.
- Salzburg have lost back-to-back home games in European competition for the first time since October 2016. They were unbeaten in 19 home European games before losing to Napoli and Liverpool.
- Excluding qualifying games, English sides are unbeaten in 18 meetings with Austrian clubs in major European competition (W14 D4).
- Mohamed Salah has been involved in 27 Champions League goals for Liverpool (19 goals, eight assists) - only Lionel Messi (28) has been involved in more since the Egyptian joined the Reds in 2017.
Man of the match - Sadio Mane
Liverpool turn their attention back to trying to win their first Premier League title. They host Watford at 12:30 GMT on Saturday looking to maintain or extend their eight-point lead at the top.
- 16JunuzovicSubstituted forDakaat 68'minutes
- 14SzoboszlaiSubstituted forAshimeruat 90'minutes
- 30HaalandSubstituted forOkugawaat 75'minutes
- 9Hwang Hee-Chan
- 6LovrenSubstituted forGomezat 53'minutes
- 4van Dijk
- 8KeitaSubstituted forOrigiat 87'minutes
- 9FirminoSubstituted forMilnerat 75'minutes
- 10ManéBooked at 51mins
- Danny Makkelie
- Shots on Target
Second Half ends, FC Red Bull Salzburg 0, Liverpool 2.
Attempt missed. Mohamed Salah (Liverpool) left footed shot from the centre of the box misses to the right. Assisted by Georginio Wijnaldum following a fast break.
Attempt missed. Sadio Mané (Liverpool) header from the centre of the box misses to the left. Assisted by Trent Alexander-Arnold with a cross following a corner.
Substitution, FC Red Bull Salzburg. Majeed Ashimeru replaces Dominik Szoboszlai.
Corner, Liverpool. Conceded by Maximilian Wöber.
Attempt blocked. Sadio Mané (Liverpool) right footed shot from the centre of the box is blocked. Assisted by Jordan Henderson with a cross.
Substitution, Liverpool. Divock Origi replaces Naby Keita.
Offside, FC Red Bull Salzburg. Cican Stankovic tries a through ball, but Patson Daka is caught offside.
Offside, Liverpool. Georginio Wijnaldum tries a through ball, but Mohamed Salah is caught offside.
Attempt saved. Sadio Mané (Liverpool) left footed shot from the centre of the box is saved in the bottom left corner. Assisted by Mohamed Salah.
Attempt missed. Sadio Mané (Liverpool) header from the centre of the box misses to the right. Assisted by Trent Alexander-Arnold with a cross following a corner.
Attempt blocked. Mohamed Salah (Liverpool) left footed shot from outside the box is blocked. Assisted by Naby Keita.
Corner, Liverpool. Conceded by Jerôme Onguéné.
Attempt missed. Mohamed Salah (Liverpool) left footed shot from outside the box misses to the right following a corner.
Corner, Liverpool. Conceded by Andreas Ulmer.
Attempt saved. Mohamed Salah (Liverpool) left footed shot from the right side of the box is saved in the centre of the goal. Assisted by Jordan Henderson.
Substitution, FC Red Bull Salzburg. Masaya Okugawa replaces Erling Haaland.
Substitution, Liverpool. James Milner replaces Roberto Firmino.
Attempt missed. Roberto Firmino (Liverpool) right footed shot from a difficult angle on the left is close, but misses to the left. Assisted by Sadio Mané.