Seedorf's brace came shortly after the Brazil federation's disciplinary tribunal slapped the ban on Cruzeiro after missiles were thrown onto the pitch at their match against neighbours Atletico Mineiro last month, halting play for 10 minutes.
The Foxes will have to play their Brazilian championship games at least 100 kilometres from their base in Belo Horizonte.
Three directors were banned for 30 days each for running onto the pitch to protest to the referee in the same match while midfielder Leandro Guerreiro, sent off for fighting, was suspended for two games.
Only fans of Cruzeiro, officially the home team, had been allowed to watch the game in an attempt to stop violence which has plagued their fixtures against Mineiro.
Tinga put Cruzeiro ahead after 20 minutes of on Wednesday's match but two goals in two minutes from former AC Milan midfielder Seedorf gave Botafogo a 2-1 halftime lead.
The 36-year-old Seedorf also set up the third goal as he burst down the left and crossed for Jadson to complete the scoring.
Mineiro, the championship leaders, completed their fourth game without a win as they drew 0-0 at lowly Bahia without Ronaldinho, who was suspended.
The Roosters have 45 points, one more than former Real Madrid and Brazil coach Vanderley Luxemburgo's Gremio, who claimed a 2-1 win over bottom club Atletico Goianiense.
Two goals from former Shakhtar Donetsk, Manchester City and Galatasaray midfielder Elano were enough for the Porto Alegre team.
Figueirense moved off the bottom of the table with a 1-0 win over South American champions Corinthians.