Host Goianiense took the lead through Marcio's 28th-minute penalty but 36-year-old Seedorf, who joined Botafogo last month, levelled up the scores in the 65th minute with his first goal for the club.
Fellype Gabriel then netted a 75th-minute winner for the visitor as Botafogo climbed into the top six of the Brazilian Campeonato.
Internacional is three points above Botafogo in fourth place after earning a 1-0 win at Palmeiras,
In the other match, Portuguesa beat 10-man Figueirense 2-0 through goals from
Santos has ended talks with Marcelo Bielsa to become its new coach.