The Brazilian striker, who returned to the club on loan to cover the Ayew brothers' departure for the Africa Cup of Nations, scored 13 minutes after the interval to set up a final clash against Olympique Lyon.
The Cote d'Azur derby was a fierce confrontation between the two clubs who both finished with 10 men after Mathieu Valbuena and Franck Dja Djedje were sent off in the second half.
France striker Loic Remy gave Marseille an early lead when he bent the ball in from the left side of the box after 17 minutes.
But the League Cup holders were made to work hard by a combative Nice who hit back late in the first half when Anthony Mounier volleyed in a Dja Djeje pass after Remy lost the ball in his half.
Brandao secured his team's place in the final when he shot home from close range.
Marseille defended strongly and denied Nice many chances to come back despite Valbuena's sending-off with 25 minutes left when he was booked for a second time for taking a free-kick before the referee whistled.
He will miss the Ligue 1 clash against Lyon on Sunday.
The League Cup final will take place at Stade de France on April 14.
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