Mbappe net in the first half before racing away to score his second to make it 3-0 to PSG. Full-back Alessandro Florenzi scored with a header after hitting the post twice.
And Spaniard Pablo Sarabia, who set up Florenzi, made it 4-0 late on.
Nimes defender Loick Landre was sent off for a reckless challenge on Rafinha after he caught him in the stomach with his studs in the 12th minute.
Midfielder Rafinha, who joined the French champions on a three-year deal from Barcelona this month, was impressive throughout and picked up an assist before being substituted in the second half.