The first goal came on 34 minutes through Borges before substitute Willian and Ricardo Goulart struck late in the second-half to cap off the victory.
With five league games to play, Cruzeiro holds a 13-point lead over second-placed Atletico PR and will hold aloft the trophy if they triumph in Vitoria on Wednesday.
Atletico PR kept their mathematical hopes of winning the title alive with a 3-0 home victory over Sao Paulo.
Despite conceding the majority of possession, Atletico PR scored twice in the first half through Marcelo and Luiz Alberto before Ederson sealed the victory in the 58th minute.
Nautico were officially relegated as they were beaten 1-0 by fellow strugglers Criciuma.
Wellington Paulista scored the only goal of the game that sees Criciuma move within one point of safety.
The other two teams in the relegation zone both suffered defeats with Ponte Preta going down 3-0 at home against Vitoria and Fluminense losing 1-0 to Corinthians.
Vasco da Gama is one point above the relegation zone after a 2-2 home draw against Santos while Bahia is three points ahead of the drop zone after sharing the points in a goalless draw with Atletico Mineiro.
In other matches, Flamengo and Goias had a 1-1 draw, Internacional overcame Botafogo 2-1 and while Portuguesa and Coritiba played out a goalless draw.
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