Di Maria got the visitors off to a flying start in the first half before Mbappé sealed the win in the 83rd minute after the home side had two players sent off.
Mbappé, who had been out for a month with a thigh injury, came on with half an hour remaining and the France star gave Neymar a simple finish from close range in the 70th.
A second league loss of the season ended a four-match winning streak for PSG, which stayed top of Ligue 1 after seven games.
Neymar's possible return to the La Liga club seemed to be imminent during the summer transfer market but never came to fruition.
Kaka won the game's top individual honours in 2007 when he was named FIFA world player of the year and collected the Ballon d'Or after winning the Champions League with AC Milan.
Angel Di Maria's brace and Thomas Meunier's goal sealed a 3-0 win for Paris Saint-Germain over Real Madrid at the Parc des Princes on Wednesday.
Even as Neymar celebrated the last-minute winning goal, PSG ultras behind the goal where he scored still jeered him.
Neymar sat out four league games as he pushed for a move back to Barcelona during the summer transfer window.
Neymar cost PSG a world record 222 million euro in August 2018 when he joined the French club from Barcelona.
The deal is expected to put Mauro Icardi's price tag at 70 million euros if PSG pick up the option after the free loan.
Neymar attracted interest from Barcelona and Real Madrid but the former's move was rejected as it didn't meet the demands of the French outfit.
It will be tough for PSG after being paired in a group with a Real Madrid side chasing a record-extending 14th European crown.
Neymar has fully recovered from an injury he sustained in early June while on international duty with Brazil, Tuchel said during a press conference ahead of Sunday's Ligue 1 game against Toulouse.
After a 2-1 loss at Rennes on Sunday, Thomas Tuchel wearily complained his players lacked fitness due to shorter preparation time. Some were involved in the Copa America, for example, which finished on July 7.
After a 3-0 win in the first game, PSG were alarmingly bad in a 2-1 loss to Rennes. Neymar is yet to play a game for the side, and the performance against Rennes hardly inspires confidence.
Before the start of the 2019/20 season, Neymar hinted on his desire to leave PSG and reports claimed it's Barcelona where he wants to play again but the transfer saga is not easy for him.
Neymar, who left Barcelona in controversial transfer move to PSG two years ago, could make a sensational return to his former club.
PSG, still without Neymar, suffered a shock 2-1 defeat to Rennes in the Ligue 1 on Saturday, and have slipped to 8th position in the league standings.
Neymar has failed to return for pre-season training with the club, fuelling talk of him wanting to leave the club after he was roped in for a world record fee two years ago.
Barcelona have not hidden their interest in the Brazilian's return after PSG decided to put his services up for sale.
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