Mineiro striker Carlos netted his second of the match in the 91st minute to upset the defending champions, who had rallied from two goals down at the Estadio Governador Magalhaes Pinto.
League leaders Cruzeiro were comfortable 3-2 winners against Atletico PR on Wednesday, but they found it difficult against sixth-placed Mineiro over the weekend.
The first half was on track to end all square, before Mineiro netted two goals in as many minutes through Carlos and Diego Tardelli.
Mineiro striker Carlos broke the deadlock in the 39th minute, volleying the ball past Cruzeiro goalkeeper Fabio after Luan's deflected header fell into his path.
And Tardelli doubled the visitors lead two minutes later, when he got on the end of Jesus Datolo's outside-of-the-foot cross, volleying from close range.
The home side were on level terms seven minutes into the second half thanks to Alisson, whose bicycle kick left Mineiro custodian Victor helpless.
After recording back-to-back wins, Mineiro have 37 points from 23 matches.
Sao Paulo twice surrendered a lead as they lost 3-2 at fourth-placed Corinthians - their second loss in the space of a week following Wednesday's 3-1 defeat to Coritiba.
Goals from Souza and Edson Silva, sandwiched between Fabio Santos' penalty, had Sao Paulo leading 2-1 at half-time.
But it all fell apart after the break, with Alvaro Pereira's second yellow card leading to a penalty in the 66th minute and sparking a collapse.
Gremio's resurgence under Luiz Felipe Scolari continued against Chapecoense, winning 1-0.
Scolari's men sit fifth in the standings after seven games without defeat and six successive clean sheets.
