Brandao, who came on as a late substitute in a drab final at the Stade de France, scored in the 105th minute with an angled shot from a cross by Benoit Cheyrou to secure his team a berth in next season's Europa League playoffs.
The result ended Marseille's dreadful sequence of 12 matches in all competitions without a win, 11 of them defeats.
"It does not change the fact we're having a bad season but it's a trophy and nobody can take that away from me, not even my worst enemies," Marseille coach Didier Deschamps told a news conference.
"I told the players to be positive. They did what they had to do and they deserve this trophy," he added.
Mathieu Valbuena's curling shot from the edge of the box on 62 minutes then went wide as Marseille looked to take control of a game littered with fouls.
They also went close in the 65th minute when Morgan Amalfitano's header from a Valbuena cross was deflected on to his right post by keeper Hugo Lloris.
The Brazilian, who went back to Marseille in January after loan spells in his native country, was on the receiving end of Cheyrou's centre from the left and coolly slotted the ball home.
"We were timid, we made a lot of mistakes but Marseille also did not let us play our game," said Lyon coach Remi Garde. "We were not efficient enough and some of my players were not fresh enough.
"We still have two objectives," he said, referring to the French Cup final and fourth-placed Lyon's bid to clinch third position in Ligue 1 - a finish that would give them a Champions League play-off spot next season.
