Luciano came off the bench and scored the match-winning goal in the 73rd minute at Estadio Governador Magalhaes Pinto in Belo Horizonte.
Cruzeiro were weakened, with Everton Ribeiro on international duty with Brazil and star striker Ricardo Goulart injured.
And Corinthians seized the opportunity, despite losing two key players of their own to Brazil coach Dunga - Gil and Elias.
Despite Kaka's absence due to Brazil commitments, Sao Paulo won thanks to Maicon's sixth-minute goal, with the midfielder curling into the top-left corner in style.
Sao Paulo are two points ahead of Internacional, in third, after they were embarrassed 5-0 at lowly Chapecoense on Thursday.
Diones and Leandro both scored twice in Chapecoense's shock win, as they climbed out of the relegation zone.
Henrique's 50th-minute strike was enough for Palmeiras to climb three points clear of the drop zone, while Botafogo remain at the foot of the table.
Flamengo ended their five-game winless streak, prevailing 2-1 at Figueirense, while Goias overturned a two-goal first-half deficit as they earned a dramatic 2-2 draw against Vitoria.
