Liverpool were beaten 2-1 by PSG in their penultimate Champions League game to leave their hopes of reaching the knockout stages in the balance.
It took 13 minutes for PSG to take the lead at the Parc des Princes as Juan Bernat swept home at the near post before Neymar (37) slotted home after Edinson Cavani's flick was saved by Alisson.
James Milner (45+1) pulled a goal back for Liverpool just before the break after the visitors were given a penalty when Angel Di Maria fouled Sadio Mane in the area.
But neither side could find another goal in the second half and Group C will go down to the final matchday in two weeks' time, with Liverpool needing to beat Napoli 1-0 or by two clear goals to make it into the knockout rounds.
PSG: Buffon (6), Kehrer, Thiago Silva (7), Kimpembe (6), Bernat (7), Verratti (7), Marquinhos (8), Mbappe (7), Neymar (7), Di Maria (7), Cavani (6).
Subs used: Alves (6), Choupo-Moting (5), Rabiot (5).
Liverpool: Alisson (7), Gomez (7), Lovren (6), Van Dijk (7), Robertson (7), Milner (7), Henderson (6), Wijnaldum (6), Mane (6), Salah (5), Firmino (5).
Subs used: Keita (5), Sturridge (4), Shaqiri (5).
Man of the match: Marquinhos.
Alisson made a leaping save from a curling Di Maria effort in the sixth minute, but could not keep out PSG seven minutes later. Kylian Mbappe's cross into the area was initially headed away by Virgil van Dijk, but the rebound fell to Bernat, who took a few strides before slotting home into the bottom corner.
The Liverpool goalkeeper was kept busy and made another fine save just after the half an hour mark. Neymar slipped Mbappe in down the left-hand side, before the Frenchman crossed into the box for the incoming Cavani. But Alisson read the situation well and came out to collect the ball ahead of the striker.
But PSG doubled their lead in the 37th minute with a spellbinding breakaway. Neymar and Mbappe played a wonderful give and go as the Brazilian sped down the field before playing in his team-mate on the left. Mbappe once again cut the ball into the area for Cavani - whose attempt to backheel the ball home was saved by Alisson - but Neymar was waiting to tap the ball home through the legs of Andrew Robertson.
PSG made four changes with Kylian Mbappe, Neymar, Thilo Kehrer and Juan Bernat coming into the XI. Liverpool made two changes as Jose Gomez and James Milner returned to the starting line-up in place of Trent Alexander-Arnold and Xherdan Shaqiri.
Liverpool came roaring back into the game on the stroke of half-time when they were awarded a penalty after Di Maria launched into a tackle on Mane in the area. Although referee Szymon Marciniak initially awarded a corner, he was correctly overruled by his assistants - much to the annoyance of the PSG players - and Milner stepped up to hammer home past Gianluigi Buffon and halve the deficit.
PSG thought they had got a third within three minutes of the restart, but Marquinhos had his effort disallowed for offside. Di Maria whipped a free kick in front of the wall, which the Brazilian poked home with an outstretched foot, but the linesman correctly had his flag raised
The second half lacked the chances seen in the opening 45 minutes but PSG saw the better efforts in front of goal and Alisson made another good save in the 70th minute. Neymar delivered a corner and it was Marquinhos again who rose highest to meet it, but his bullet header was pushed away by the goalkeeper with Mbappe unable to net the rebound.
There were jubilant scenes from the PSG players and staff at full-time and some unwanted history for Liverpool, who have lost all three of their away group games in the Champions League for the first time.
- Paris Saint-Germain have 50 Champions League wins in just 95 games; only Real Madrid (88) and Barcelona (93) have done it quicker.
- Liverpool have lost four successive European Cup/Champions League away games for the first time in their history.
- Paris Saint-Germain are unbeaten in their last 21 home group stage games in the Champions League (W16 D5), since losing 1-3 to CSKA Moscow in December 2004.
- Since 2016-17, no Champions League side have conceded more goals from the penalty spot (7) or conceded more penalties (8) than Paris Saint-Germain.
Man of the match - Marquinhos
It was a superb performance from the Brazilian, who put in a shift at both ends. Despite the attacking prowess on the field, he had the two best PSG chances in the second half but also did a good job in keeping Liverpool mostly quiet at the other end.
Indeed, in the 87th minute, as PSG strode towards victory, he helped countryman Thiago Silva see a ball out in front of Mohamed Salah, with a huge roar and chest bump with the PSG captain afterwards. It epitomised the job he had done throughout and he had a big hand in the result.
PSG travel to Bordeaux in Ligue 1 on Sunday and play their final Champions League match away to Red Star Belgrade on Tuesday 11 December. It's a huge game for Liverpool on Sunday as they host city rivals Everton, live on Sky Sports from 4pm. Their next Champions League game will be at home to Napoli on December 11.