Nilton put Cruzeiro ahead just before halftime when he managed to hook the ball in with an unorthodox volley following a corner.
Former AC Milan and Real Madrid midfielder Seedorf, 37, had the chance to equalise when Botafogo were awarded a penalty after the break but the Dutchman rolled a weak effort past the left-hand post.
Former AS Roma, Malaga and Real Madrid forward Julio Baptista then came off the bench to score two more goals for Cruzeiro, the first from the penalty spot.
"I'm sorry for the penalty, which was at an important moment in the match," Seedorf told reporters.
Botafogo said on Twitter that their bus was attacked as it entered the stadium and showed a photograph of a broken window.
Cruzeiro have 49 points from 22 games, seven ahead of Botafogo, with Gremio a further four points behind in third after their 1-1 draw at home to Santos.
Vasco da Gama dropped into the bottom four after slumping to a defeat against Vitoria.
The team known as "Dried Cod" led from the seventh minute when Andre turned in Wagner's cross but it all went wrong when Alemao equalised with 10 minutes left and Marquinhos scored an 89th minute winner.
After the equaliser, video images showed angry fans surrounding the VIP box to remonstrate with president Roberto Dinamite and the 1978 World Cup striker eventually left his seat.
Media reports said that more fans protested outside the main entrance, letting off fireworks, and players left the stadium by an alternative exit.
Despite all the trouble, only 5,240 people watched the game at Rio de Janeiro's Sao Januario stadium.
Sao Paulo chalked up their third win in eight days under new coach Muricy Ramalho, this time beating South American champions Atletico Mineiro 1-0 with a goal by Welliton.
Ramalho, who led Sao Paulo to three successive Brazilian championship titles in his previous spell at the club, returned for a third stint after Paulo Autuori was fired after 13 games with the team in the relegation zone.
The latest win moved Sao Paulo up to 13th although they are still only three points clear of the danger area.
(Writing by Brian Homewood in Berne; Editing by John O'Brien)
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