Sao Paulo, who began the day top and with a chance of clinching a fourth successive title, dropped to fourth on goal difference after a 4-2 defeat away to Goias allowed Internacional and Palmeiras to overtake them.
Inter won 2-1 away to relegated Sport Recife and Palmeiras beat Atletico Mineiro 3-1 at home to join Sao Paulo on 62 points, two fewer than Flamengo.
Brazil's most popular team are at home to Gremio at the Maracana on the final day next Sunday.
"We must continue with the same luck, the same work, the same dedication, that's how we got here and now we mustn't change anything. God willing, we'll get a win at home and be champions," said Flamengo's Serbian midfielder Dejan Petkovic.
Ze Roberto put Flamengo ahead just before the half hour from midfielder Toro's 50-metre pass and they scored again in stoppage time when full back Leo Moura converted a penalty after he had been brought down.
Corinthians' former world player of the year Ronaldo, a Flamengo fan, did little in the short time he was on the pitch before coming off with a thigh muscle injury midway through the first half.
"Football is full of surprises, as happened this weekend, so I prefer not to depend on numbers and prepare my team for what will be a very tough match against Gremio," said Andrade, Flamengo's former assistant coach who has been in charge since Cuca's resignation in July.
Santo Andre still have a slim mathematical chance of staying up after beating Nautico 5-3 in a battle between relegation rivals that ended the losers' survival hopes.
