In a one-sided contest, Neymar set the hosts on their way with an exquisite free-kick which found the bottom left corner from 25 yards out.

The Brazil forward doubled PSG's lead less than three minutes later as the visitors attempted to regroup - guiding a close-range effort into the roof of the net after exchanging passes with Kylian Mbappe.

Edinson Cavani's deflected strike made it three and Angel di Maria flicked Thomas Meunier's cross in for a fourth goal before half-time.

PSG began the competition with a narrow 3-2 defeat at Liverpool but back in Paris, and with Italian midfielder Marco Verratti restored to their starting XI after suspension, this showing was a reminder of the firepower at Thomas Tuchel's disposal.

Despite a determined start, Red Star manager Vladan Milojevic was forced into changes of personnel and tactics at the interval in an attempt to avoid embarrassment.

However, the second period continued in the same fashion as the first.

Visiting goalkeeper Milan Borjan superbly saved a succession of shots as the French Ligue 1 leaders repeatedly carved Red Star open down the left.

On his 50th appearance for PSG, Mbappe received his reward for a fine individual performance by finishing off a sublime move involving Neymar and Juan Bernat to record his 27th goal for the club.

Former Germany international Marko Marin got the Serbian side on the scoresheet with a powerful drive but Neymar had the final word with another superb free-kick.

It ensured he completed his second ever Champions League hat-trick, after one for Barcelona in their 6-1 group stage home win against Celtic in December 2013, and also became the joint-highest scoring Brazilian in Champions League history, level with Kaka on 30 goals.

Verratti the conductor

While the story of this match could easily focus again upon the exploits of Neymar and Mbappe, the two most expensive players on the planet with combined fees of £365.7m, the influence of Verratti on Tuchel's team should not be overlooked.

The 25-year-old Italian was missing as PSG lost at Anfield but back in the starting XI for this fixture, his influence shone through as he laid the platform for a dominant display.

The diminutive Italian set the tone in the opening half-hour, encouraging his team-mates to press high up the pitch and retrieving possession more than any other player.

While Red Star attempted to deploy the same tactics, Verratti's calmness on the ball and ability to pass his way out of tight situations neutralised that tactic.

The Italian also played his part in PSG's first goal, scampering through midfield and setting Neymar away to earn the free-kick from which he scored.

And his range of passing was evident throughout as he played the role of midfield conductor, making more passes and taking more touches than any other player while maintaining a 92.3% pass completion rate.

Red Star outclassed

Red Star had arrived in Paris with a seven-point lead at the top of the Serbian SuperLiga and boasting an unbeaten record stretching back 34 games to a 1-0 defeat by CSKA Moscow in last season's Europa League. This assignment, however, proved a step-up in class.

The Serbs earned their place in European football folklore by winning the competition in 1991, when they beat Marseille in the final on penalties.

But while that team was blessed with supremely talented individuals like Vladimir Jugovic, Robert Prosinecki, Sinisa Mihajlovic and Dejan Savicevic, current boss Milojevic is unable to call on of stars of that calibre.

Marin - persuaded to join the club by their first appearance in the group stages since the Champions League rebrand in 1992-1993 - is their most recognisable player. And the draw they earned against Napoli in their opening game in Group C was a resolute, collective effort.

Here, once Neymar's first free-kick of the evening had given the advantage to PSG, the visitors' game-plan largely fell away as they simply lacked the discipline to keep Tuchel's side at bay.

Man of the match - Neymar (Paris St-Germain)

Verratti or Mbappe could as easily have got the nod, but Neymar's hat-trick means he has now scored 10 goals in nine competitive games for PSG this season

Prolific PSG - the stats

• Paris St-Germain have won by four or more goals on five occasions in the Champions League since the start of last season, more than any other side in the competition.
• PSG have not lost a Champions League group stage game in Paris since December 2004 against CSKA Moscow (1-3), winning 15 of their past 19 such matches since (D4) - including victories in each of their past four.
• PSG have scored in each of their past 18 Champions League games, the longest current run in the competition.
• Neymar is the first player to score two direct free-kicks in a Champions League game since Cristiano Ronaldo v Zurich in September 2009.
• PSG's Kylian Mbappe has been directly involved in 16 goals in his 16 Champions League starts (12 goals, 4 assists).

What's next?

Paris St-Germain welcome Lyon to the Parc des Princes on Sunday 7 October (20:00 BST) in their final game before the international break. Their next Champions League fixture is at home to Napoli on 24 October (20:00 BST).

Red Star Belgrade travel to Zemun in the Serbian SuperLiga on Sunday (12:00) BST) and travel to Anfield to face Liverpool in their next Champions League assignment on 24 October (20:00 BST).