Midfielder Matteo Guendouzi scored the only goal of the game in the 59th minute following good work by Jordan Veretout.
Marseille have not won the French Cup since 1989. However, they were roared to victory at the Stade Velodrome by a 57,000-strong crowd against a Rennes side who stunned Paris Saint-Germain in Ligue 1 last weekend.
"It's a different victory to the others because we were in a knockout game," said Marseille coach Igor Tudor.
"The players were very motivated and they interpreted the game very well, against a good team."