Two goals from young striker Bernard helped Mineiro end a run of four matches without a win and strengthened the side's grip on second place, two points behind leaders Fluminense with a game in hand.
The loss leaves Palmeiras, coached by former Brazil and Portugal manager Luiz Felipe Scolari, 30 points behind the leaders and five adrift of Coritiba, the lowest-placed team outside the relegation zone.
Despite struggling in the league, the Copa Brasil victory has already ensured Palmeiras a berth in the South American Libertadores Cup next year but the side will be hoping to climb out of trouble in the final 15 games of the season.
On a weekend when many leading players were absent on international duty, Santos and Sao Paulo served up a disappointing 0-0 draw in their "clasico" at the Vila Belmiro in front of a paltry crowd of less than 7,000.
Santos idol Neymar, team-mate Arouca and Sao Paulo midfielder Lucas were unavailable as they prepared for Brazil's friendly against China in Recife on Monday, while Santos playmaker Ganso was out through injury.
Both clubs also lost players to Brazil's Olympic team during the recent London Games.
Fluminense beat Internacional 1-0 away in front of another small crowd of around 7,000 at the Beira-Rio in Porto Alegre, most of which is closed while construction work for the 2014 World Cup is being carried out.
Striker Fred scored the only goal of the game after some fine approach play by winger Wellington Nem against an Inter side missing Brazil striker Leandro Damiao, Uruguay's Diego Forlan and Argentina midfielder Pablo Guinazu.
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