The 36-year-old Dutchman, described by Botafogo president Mauricio Assuncao as the greatest foreign player to sign for a Brazilian club, produced a subdued performance, although he was applauded by home supporters on being substituted late in the game.
"The atmosphere was amazing, I hope every game is like that," the former AC Milan, Inter Milan, Real Madrid and Ajax midfielder said after the game.
"Seedorf has only been with us for two weeks," said coach Oswaldo de Oliveira. "He's at the start of the season and we're in the middle."
Botafogo are eighth in the 20-team table with 17 points from 11 games.
There were mixed fortunes for the three teams who fired their coaches on Friday.
Bahia, who dismissed former Brazil midfielder and coach Paulo Roberto Falcao, squandered a 2-0 lead and drew 2-2 at home to Coritiba under interim coach Eduardo Barroca with new coach Caio Junior watching from the standards.
Internacional gave new coach Fernandao, who replaced Dorival Junior, a 4-1 win over Atletico Goianense.
Figueirense, who dismissed Argel on Friday, went down to a 2-0 home defeat against Sao Paulo, who notched their first win under Ney Franco.
Figueirense supporters responded to their team's performance by turning their backs to the pitch en masse during the second half.
A 4-1 win at Sport Recife kept Atletico Mineiro top of the table, two points clear of Vasco da Gama who beat Santos 2-0.