PSG had defender Dani Alves sent off in the 57th minute but seemed assured of securing a point until Depay decided otherwise with about 30 seconds left.
PSG is 11 points clear of second-place Lyon at the top. Marseille is 12 behind while defending champion Monaco trails by 13 in fourth spot.
The bizarre incident happened moments from the end of Paris Saint-Germain's 1-0 win at Nantes.
Neymar became the most expensive footballer in history when he joined the Ligue 1 outfit in August in a deal worth 222 million euros from FC Barcelona.
The 25-year-old said the fixture depends upon the performance of the whole team and not just him as an individual.
PSG have won their four matches so far in Group B - scoring 17 goals while conceding none - and are three points clear of Bayern Munich.
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.
Neymar is accused of evading 20.04 million US dollars in taxes from 2011 to 2013 by using front companies to hide the true value of his income.
Edin Dzeko's double had briefly put Roma in front but 2012 Champions League winner Chelsea remains two points ahead of the Italian club at the top of the group.
PSG players still felt pretty motivated, especially following their 3-0 home victory over Bundesliga powerhouse Bayern Munich in the Champions League group match.
Mbappe, who was hired alongside Neymar this summer, did not score but tormented the Bayern defence throughout with his dribbling ability and frenetic pace. He was decisive in setting up Neymar's goal.
The Spanish giants don't seem to miss their winger as it has been Lionel Messi who has been netting in goals consistently since the Brazilian's departure.
The 25-year-old Neymar has scored four goals and delivered four assists in five games with PSG since he joined from Barcelona in a world-record transfer worth 222 million euros ($262 million).
Neymar, who joined Barcelona in 2013 has scored 105 goals for the club, guiding them to two league titles, three Copa del Rey and a Champions League crown.
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).
Mbappe has been added to a glittering assembly of attacking talent that includes Brazil star Neymar, striker Edinson Cavani, and wingers Angel Di Maria and Julian Draxler.
With Paris Saint-Germain spending massively, French clubs paid out 697 million euros ($830 million) and made 619 million euros ($736 million).
Manchester City and PSG spent hundreds of millions of dollars in the transfer window that closed last week.
Once PSG signed Neymar, the chances of Monaco holding onto Mbappe went down.
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