PSG led early in Wednesday's crunch Group C clash when Juan Bernat capitalised on poor defending and the host doubled its 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.

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 visitor. 

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.