Brandao's goal in the 104th minute was enough to secure the trophy for Didier Deschamps's side.
Lyon nearly took the lead in the third minute, but Dejan Lovren could only put his header inches wide of the post from Kim Kallstrom's whipped free kick.
Despite the early scare, Marseille controlled much of what was a drab first half, but failed to create many clear chances in front of goal.
Remi Garde's side almost gave themselves a first-half lead when Befetimbi Gomis narrowly failed to connect with Michel Bastos's shot.
Andre Ayew's free kick was well saved by Hugo Lloris 10 minutes after the break, before Mathieu Valbuena's effort went just wide.
The best chance of the 90 minutes fell to Marseille midfielder Morgan Amalfitano, who hit the post from Valbeuna's cross.
There was still time for a final chance in normal time, but Gomis could only put his header over the bar from a corner.
Marseille finally made the breakthrough in the 104th minute when Brandao picked up a pass from Bruno Cheyrou before firing in low under Lloris.
The goalkeeper was called into action again at the start of the second period of extra time when he had to push away Ayew's diving header.
Lloris had to pull off a final save before the end of the match to deny Rod Fanni's header.
The night finished on a sour note for Lyon as Lovren was shown his second yellow card after a melee involving players from both sides.