First-half goals from Edinson Cavani and Neymar, a second-half header from Marquinhos and a late Kylian Mbappe strike were enough to send Thomas Tuchel's side into the last 16, despite Marko Gobeljic's finish 56 minutes in.
That fast pace kept up in a game that had greater tension placed upon it after news filtered through of an early PSG goal in Belgrade but with the greater sense of urgency on the hosts, they found it tough to carve out real clearcut opportunities until shortly after the half hour mark.
The PSG boss was quoted by L'Equipe as saying: 'It's super hard to win here and the guys played magnificently. When Belgrade scored, we stayed calm, patient.
Topping such a keenly-contested group is a huge boost for PSG, who have dominated French football since being taken over by Qatari investors but flattered to deceive on the continent.
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Thomas Tuchel was thrilled with Paris Saint-Germain's attitude and quality as they beat Red Star Belgrade 4-1 to reach the Champions League knockouts.
"Now, we're in the last 16".
Asked about PSG's chances of winning the Champions League, Mbappe added: "We need to see what we'll have in front of us".
PSG had Red Star on the back foot from the start, and their blistering attacking trio of Neymar, Mbappe and Cavani did not waste time in putting the away side ahead.
But there was no stopping Neymar from a dazzling finish five minutes before the break, the Brazil star collecting Mbappe's reverse pass, driving into the box and leaving Borjan on the ground with a dummy before firing home.
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The Partenopei couldn't impose themselves on Jurgen Klopp's side whatsoever, struggling against the Liverpool press and losing possession at the back and in midfield much too easily, leading to opportunities for both Jordan Henderson and James Milner.
Red Star improved after half-time and deservedly got a goal back through Gobeljic, who volleyed expertly past Gianluigi Buffon at the near post, and the visitors looked to be unsettled for a time as the home fans roared their approval.
Mbappe's neat finish as the final seconds ticked away and Liverpool's win were the icing on the cake for PSG.
"We are happy", said the France worldwide.
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