With Atletico needing a win to guarantee their progression, 22-year-old Simeone scored his first Champions League goal in the fifth minute by shooting low into the far corner from the right side of the box.

Eight minutes later, the Argentina international – one of Simeone’s three sons who are all professional footballers – crossed for Antoine Griezmann to tap in Atletico’s second to effectively seal the result.

Griezmann was thwarted by the boot of Salzburg goalkeeper Alexander Schlager late in the first half but could not be denied a second time as he slotted low across Schlager in stoppage time.

Marcos Llorente drove in Atletico’s fourth in the 63rd minute before 19-year-old Adam Daghim struck home a spectacular consolation for Salzburg in stoppage time – his first Champions League goal.

After opening with a victory, the Spanish side lost their second and third games in this season’s competition, but have since won five consecutive matches.

A tricky path still awaits, however. Despite finishing the league stage in fifth spot, they will play one of Manchester City, Real Madrid, Bayern Munich or Celtic in a mouthwatering last-16 tie.

Salzburg, already eliminated before their trip to Madrid, ended with seven defeats from eight and finished 34th.

After losing three of their opening six games, Madrid looked more like their usual selves as they dispatched the Austrians with a first-half double from Rodrygo, before a goal from Kylian Mbappe and two from Vinicius Jr followed after the break.

This win and results elsewhere guarantee Madrid at least a play-off spot, and they are one point off the automatic qualification places, with a visit to Brest on the final matchday next week.

Salzburg, whose only consolation was a late Mads Bidstrup volley, have lost six of their seven league phase games and are out of the Champions League.

They needed a win and for other results to go their way to stand a chance of sneaking into the play-offs, and started stronger at Santiago Bernabeu with Oscar Gloukh shooting narrowly wide from 18 yards.

But Madrid soon hit their straps as their biggest names turned up when it mattered.

On 23 minutes Madrid led with their first meaningful attack of the game. A sweeping move from back to front saw Jude Bellingham knock down Vinicius’ aerial ball and Rodrygo netted with an angled volley.

That lead was doubled before half-time with a beautiful strike, demonstrating Madrid are still to be feared in Europe despite their indifferent league stage form.

Rodrygo played a one-two with Bellingham, the Englishman giving the return pass with a back-heel, and the Brazilian swept home from the edge of the box.

The win was sealed three minutes after half-time when Mbappe capitalised on a mistake by visiting keeper Janis Blaswich, dispossessing the German in his six-yard area and tapping home.

Vinicius, who moved to seven goals in six Champions League games, made it 4-0 after 55 minutes, collecting a brilliant Luka Modric pass and cutting into the box from the left before curling a right-footed effort beyond Blaswich.

And he made it five with a cool finish after a Madrid passing move all the way up the pitch from goalkeeper Thibaut Courtois.

The French outfit proved far too strong for their Austrian counterparts, controlling the tempo and tone of the game from the outset.

Salzburg goalkeeper Alexander Schlager made several fine saves, including a double stop to keep out Achraf Hakimi and Goncalo Ramos, before he was eventually beaten by the latter from close range.

PSG arrived at the Red Bull Arena without a victory in four Champions League outings – their longest winless streak in the competition since a run of five in 2015 – but they played with confidence and were fully deserving of the result.

A patient approach paid dividends in the second half when Nuno Mendes grabbed PSG’s second and Salzburg’s heads dropped when Desire Doue extended the lead in the closing stages.

Victory moves PSG up one place to 24th in the standings – a position which would see them through to the play-off phase – and offers hope of playing knockout football in the Champions League for a 13th successive campaign.

PSG still have Manchester City and Stuttgart to play in January.

Salzburg remain 32nd with just one win from their six outings and close out their campaign against Real Madrid and Atletico Madrid next month.

The Czech champions’ last appearance in the competition proper came in December 2005 when they finished last in a group containing Arsenal, Ajax and FC Thun.

After such a long wait Sparta needed just 107 seconds to take the lead at home to Salzburg through Kaan Kairinen’s effort on the rebound.

Victor Olatunji doubled Sparta’s advantage shortly before half-time with a fine volleyed effort.

Qazim Laci rounded off the win in the 58th minute with a simple strike after wrong-footing two defenders and the Salzburg goalkeeper with a dummied shot.

Sparta’s win was their first in the Champions League proper since beating Lazio 1-0 in December 2003.

The 41-year-old, who joined Liverpool in 2014, will go to the Austrian club this summer on a three-year deal.

Lijnders, who is in his second stint at Anfield, had been set to leave the club following Jurgen Klopp’s decision to step down.

The Dutchman said he wants to create an attacking style of play at his new club “where passion and hunger for success are the basis of everything”.

Having initially worked under Brendan Rodgers, Lijnders remained a key part of Liverpool’s backroom staff after Klopp’s appointment in October 2015.

He left the Reds for a brief stint as manager of Dutch club NEC Nijmegen but returned to Anfield seven months later to fill his previous role.

Liverpool’s development coach Vitor Matos will join Lijnders in the Austrian top-flight team as his assistant manager.

The Poland captain, on his 100th start in the competition, confidently stroked home two penalties inside 21 minutes, after twice being recklessly brought down by Salzburg defender Maximilian Wober, the second confirmed after a VAR review.

The first spot-kick, swept into the bottom-left corner, was Lewandowski’s 40th goal of the season in all competitions.

He added his third after chasing down an attempted clearance from visiting goalkeeper Philipp Kohn to tap in from close range.

It is the first time a Champions League hat-trick has been completed as early as the 23rd minute, although it is not the quickest treble in the competition, with that record held by Bafetimbi Gomis following his three goals in eight minutes for Lyon in a 7-1 win over Dinamo Zagreb in 2011.

Bayern’s quick start put them firmly in control of a game that had been billed as “all or nothing” by some in the Bavarian media after the six-time winners were held to a disappointing 1-1 draw in the first leg in Austria.

Matthias Jaissle’s Salzburg had early chances with Nicolas Capaldo and Nicolas Seiwald both guilty of failing to convert glorious opportunities.

They were made to pay for their profligacy by the deadly Lewandowski before another mistake in defence allowed Serge Gnabry to add a fourth with a low shot that squirmed under Kohn, while Thomas Muller thumped in a fifth after the break.

On an otherwise bleak night for the visitors, Maurits Kjaergaard did at least manage a consolation with a powerful effort into the top-left corner.

But that only seemed to stir Julian Nagelsmann’s team back into life, with Muller finishing off a well-worked move for number six before Leroy Sane thumped home late on.

The Bavarians, who have won five titles in 2020 including the Champions League, went behind after only four minutes when Mergim Berisha was left completely unmarked inside the box to beat goalkeeper Manuel Neuer.

Bayern instantly bounced back and Serge Gnabry had his shot cleared off the line before their top scorer Lewandowski levelled with a 21st-minute penalty.

Salzburg defender Rasmus Kristensen then turned a Thomas Muller cross into his own net a minute before the break.

The hosts came close to an equaliser right after the restart but Neuer got his fingertips to Enock Mwepu’s shot to turn it wide. The Bayern keeper was beaten in the 66th minute, however, when Masaya Okugawa fired Salzburg level.

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Despite a string of chances for the home side, it was Bayern who scored again in a strong finish with Jerome Boateng powering in a header from Joshua Kimmich’s corner in the 79th and Leroy Sane scoring with a perfectly curled shot four minutes later.

Lewandowski headed his second goal in the 88th and Lucas Hernandez drilled in a sixth in stoppage time to lift Bayern to nine points in Group A ahead of second-placed Atletico Madrid.

Lokomotiv Moscow, who drew 1-1 at home to Atletico, are third on two, with Salzburg in last place on one.