With Neymar having a quiet game and missing a late chance, it was left to Cavani and playmaker Javier Pastore to shatter one of the league's best defences.
Draxler set up Cavani for the fourth goal and his 101st in just 144 games, with a pass from the right following a quick PSG counterattack an hour in.
Having netted a career-high 49 goals in all competitions last season, Cavani already has 11 league goals in 10 games and 15 in 13 overall.
Cavani won the foul after being knocked over by forward Bouna Sarr, and curled the ball in off the underside of the crossbar in injury time to salvage a draw.
PSG was without Edinson Cavani left out after playing for Uruguay in World Cup qualifying this week but carved out enough chances to win easily.
The 18-year-old striker started the game in a PSG attack also featuring Edinson Cavani and Brazil star Neymar, who joined this summer from Barcelona for a world record 222 million euros ($262 million).
With Paris Saint-Germain spending massively, French clubs paid out 697 million euros ($830 million) and made 619 million euros ($736 million).
Once PSG signed Neymar, the chances of Monaco holding onto Mbappe went down.
As the transfer window closes this month, Europe's giants are still on the look out for players from different clubs.
Although Neymar did not add to his three goals, his free kick led to PSG's second goal, which was scored by midfielder Thiago Motta.
Neymar was "stunned" by the legal action Barcelona had taken against him and confirmed he would seek the second payment be made by the club.
In a statement released by the officials, PSG reiterated that they have done nothing wrong regarding the Brazilian's transfer from Camp Nou.
Besides Neymar, Emery said summer signing Dani Alves has improved his group from last season in certain areas.
Since joining in July 2011, Matuidi has played 295 games for Paris Saint-Germain, seventh overall in the club's history, scoring 33 goals and dishing out 30 assists.
Neymar looked intensely focused from the start, easily switching from one wing to the other, and often taking a playmaker role.
The 25-year-old ace Brazillian ace is now expected to make his debut for PSG on Aug. 13 against Guingamp.
PSG said Neymar would have been included in the squad if the document had been submitted in time. The former Barcelona star had said he was ready to play during his first press conference in Paris.
The Brazilian star flew in from Barcelona on a private jet for his official presentation, arriving in a city whose soccer fortunes he is expected to transform.
Neymar is poised to become an even better player in Paris than the one who has dazzled Camp Nou with his lightning-quick feet and flair for beautiful goals.
Neymar is expected in Paris in the coming days.
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