Cavani and Neymar were both assisted by their 19-year-old teammate, with Mbappe putting on an excellent display of speed, strength and dribbling throughout the game.
Paris Saint-Germain will play Liverpool on Wednesday in their Champions League fixture at the Parc des Princes.
PSG's 12th straight win from the start of the season is a record for the top five European leagues, beating Tottenham's 11 opening wins in 1960.
The last player to win the trophy before Ronaldo and Messi took over was Kaka in 2007.
Mbappe won the best young player award at the World Cup in Russia after becoming the first teenager to score in a final since Pele in 1958, delivered his most efficient display since joining PSG against Lyon.
The 19-year-old striker, a member of the France squad which won the World Cup in July, received a red card in stoppage time during PSG's 4-2 win over Nimes.
With seconds remaining, Mbappe reacted to a late challenge from midfielder Teji Savanier and shoved the player forcefully to the ground.
Kylian Mbappe, who became the first teenager to score in World Cup since Brazilian legend Pele, is giving his bonus to an association that puts sports in the lives of hospitalised children.
The victory came at a time when many French were in need of good news, and the magic provided a sense that a grand coming together might at least paper over political, economic and social fissures for a while.
About two-thirds of Les Bleus' roster included players with immigrant backgrounds, a mini-United Nations of soccer talent.
At the US-Canada-Mexico World Cup in 2026, Mbappe will be in his polished prime, at age 27.
Kylian Mbappe and France put on a thrilling show in winning the World Cup title.
France have clinched their second World Cup title with a 4-2 win over Croatia in a dramatic final in Moscow.
They have impressed audiences with their great skills, superb goals and have shown the world that they are the future stars.
The denial comes two days after Madrid dismissed a report that they had offered to buy Neymar from PSG for a world record transfer of 310 million euros ($360 million).
At 19 years and 183 days, Mbappe became the youngest scorer in France's World Cup history.
France missed several first-half chances and was punished in the 44th when the U.S. scored with its first meaningful attack through forward Julian Green.
The unofficial 'Golden Boy' award has given a platform to many budding and young players such as Cesc Fabregas, Sergio Aguero and Lionel Messi since 2003.
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