Palmeiras rallied with two late goals to spoil Neymar's 20th birthday celebrations and 100th career goal on Sunday in the Sao Paulo state championship.
In the Rio de Janeiro state championship, Vasco da Gama won its fourth in a row and Flamengo and Botafogo played each other to a scoreless draw.
There were fights between fans before three matches throughout Brazil on Sunday, but no serious injuries were reported.
Neymar, touted as Brazil's most promising star and the player who will likely be in charge of leading Brazil at the 2014 World Cup at home, scored for the 100th time with a header in the 66th minute. He easily found the net from the six-meter (yard) line after a free kick cross from play maker Paulo Henrique Ganso.
But two-time defending champion Santos went a man down in the 87th after substitute striker Ibson was sent off with a second yellow card, and Palmeiras took advantage with quick goals in the final minutes.
Striker Fernandao scored with a header off a corner in the 89th, then left back Juninho put Palmeiras the go-ahead goal two minutes into injury time after his low cross was deflected by a defender as goalkeeper Rafael dove the wrong way.
Palmeiras got the win despite playing without Chile playmaker Jorge Valdivia from the 40th because of an apparent muscle injury.
Palmeiras and Santos are Brazil's most successful clubs with eight national titles each.
Before the match, local media reported that Palmeiras fans were attacked by a group of Corinthians supporters as they left for the match in Sao Paulo. The Corinthians fans reportedly threw rocks at the buses carrying Palmeiras fans. Nobody was seriously injured but police made nearly 20 arrests.
The result kept Luiz Felipe Scolari's side unbeaten in the regional championship and moved it to fourth in the 20-team standings with 11 points. Santos dropped to 10th. The top eight will advance to the knockout round.
The Brazilian football season does not follow the European calendar and starts in the beginning of the year. Regional championships in the 26 states take place in the first few months, with the Brazilian league running from May until December.
Also Sunday, Corinthians lost its first points of the season by drawing Bragantino 1-1 at Pacaembu stadium in Sao Paulo. The Brazilian champion had won its first four matches to start the season.
Corinthians still leads the tournament with 13 points, the same number as Paulista, which on Saturday defeated Catanduvense 3-1 in Jundiai, and Sao Paulo, which beat Ponte Preta 3-1 in Campinas on Sunday.
Fans from Sao Paulo and Ponte Preta engaged in a confrontation with each other and police before the match, and officers had to use rubber bullets to disperse the crowd, according to local media. A few minor injuries were reported.
In Rio de Janeiro, Ronaldinho's Flamengo and Botafogo played to a 0-0 draw at the Engenhao stadium in the Guanabara Cup.
Flamengo held on to the score despite playing a man down from the 72nd because midfielder Willians was sent off after complaining with the referee for being awarded a yellow card.
Botafogo had Argentine German Herrera and Uruguayan Sebastian "El Loco" Abreu on attack.
Flamengo was without a coach after former Brazil manager Vanderlei Luxemburgo was fired on Thursday following a series of disputes with club directors and some players, including two-time FIFA player of the year Ronaldinho.
Both teams are winless in three matches in the tournament.
The Guanabara Cup is the first stage of the Rio championship, and its winner will play for the state title against the Rio Cup champion later in the tournament.
On Saturday, playmaker Diego Souza scored twice to give Vasco da Gama -- runner-up to Corinthians in the Brazilian league last year -- a 2-0 win over Friburguense at Sao Januario stadium. It was the team's fourth win in a row to start the season.
Fluminense drew Duque de Caxias 1-1 in Volta Redonda on Saturday in the return of midfielder Thiago Neves.
In Porto Alegre, rivals Gremio and Internacional drew 2-2 in the Rio Grande do Sul state tournament. Earlier in the day, Gremio striker Kleber was accused by his wife in a police report of allegedly hitting her last month, according to local media. Police said they would investigate.
International fan groups fought each other near the stadium before the match, but no injuries were reported.