Neymar scored the decisive goal in a 2-1 home win for Paris Saint-Germain that leaves Liverpool on the brink of an early Champions League exit.
PSG led early in Wednesday's crunch Group C clash when Juan Bernat capitalised on poor defending and the hosts doubled their advantage through a record-breaking Neymar goal.
His close-range finish on the rebound was Neymar's 31st Champions League goal, moving him clear of Kaka as the most prolific Brazilian in the competition's history.
James Milner scored a penalty on his 150th Liverpool appearance but Jurgen Klopp's side could not find a crucial equaliser at the Parc des Princes and they must now beat pool leaders Napoli at Anfield on matchday six to have any chance of progression.
C'EST FAIT ! Le Paris Saint-Germain s'impose face aux Reds (2-1) ! MAGNIFIQUE !! November 28, 2018
Angel Di Maria forced an early save from Alisson and the goalkeeper was soon in action again, Neymar firing straight at his fellow Brazil international.
Alisson was beaten in the 13th minute, though, Bernat rifling into the bottom-left corner after seizing on a loose clearance from Virgil van Dijk.
Mohamed Salah fired wide before Marco Verratti was perhaps fortunate only to be booked for a high tackle on Joe Gomez.
PSG made it 2-0 as Neymar tucked in the rebound when Edinson Cavani's poor finish was saved by Alisson after a rapid attack, but Liverpool got one back from the spot before the break.
Sadio Mane went to ground under Di Maria's challenge, referee Szymon Marciniak initially giving a corner before changing his mind, and Milner sent Gianluigi Buffon the wrong way.
Marquinhos had a third for PSG rightly ruled out for offside shortly after the restart and Roberto Firmino wasted a good headed chance for the visitors.
Klopp threw on attacking substitutes Daniel Sturridge and Xherdan Shaqiri in search of a leveller, but PSG held on to gain revenge for September's dramatic 3-2 loss at Anfield.
Neymar surpasses Kaká to become the all-time leading Brazilian goalscorer in the in his 52nd game November 28, 2018
What does it mean? Liverpool in trouble
Last season's beaten finalists are not out yet but they have a tough task to book a place in the knockout rounds of the Champions League. Group C leaders Napoli visit Anfield and Liverpool must win that match to progress instead of Carlo Ancelotti's side.
Neymar dazzles on grand stage
The jewel in PSG's expensively assembled crown has not always produced his best performances when his team needed them, but Liverpool could not handle Neymar. The Brazilian caused endless problems for the Reds defence and could have easily had more than his solitary history-making goal to show for his excellent efforts, with Van Dijk possibly lucky not to concede a late penalty.
Henderson loses Verratti battle
Liverpool protested that Verratti should have been dismissed for a bad foul on Gomez, but the Italy international dominated midfield with a classy display. Liverpool captain Jordan Henderson, sent off at Watford at the weekend, could not get close to his direct opponent.
What's next?
On matchday six next month Liverpool host Napoli while PSG will look to seal qualification away to Red Star. The Reds play Everton in the Merseyside derby at Anfield on Sunday, when PSG head to Bordeaux.
