Leaders Sao Paulo, who had won four of their previous five matches, went down 3-2 to relegation-threatened Botafogo in Rio earlier in the day.
Flamengo failed to find a way past Goias keeper Harlei in front of a crowd of 84,000 at the Maracana and had to settle for a point.
Title holders Sao Paulo lead with 62 points, one more than Flamengo with two matches to go, while Internacional climbed to third with a 1-0 away win over Atletico Mineiro in Belo Horizonte.
Inter are level on 59 points with fourth-placed Palmeiras, who lost 2-0 away to Gremio in midweek.
"We haven't lost anything yet, we had to win our last three matches, we didn't manage that, but we still managed to get one point closer to Sao Paulo," said Flamengo midfielder Kleberson.
Adriano squandered Flamengo's best chance 10 minutes from the end when he shot wide from Chilean Gonzalo Fierro's cross.
RED CARDS
Botafogo striker Jobson, who scored twice, was sent off for a second booking when he took off his shirt to celebrate the last-minute winner at the Joao Havelange stadium in Rio that kept his team two points clear of the drop zone.
By then, both sides were down to 10 men after the dismissals of Sao Paulo's Richarlyson and Juninho of Botafogo. Botafogo substitute Rodrigo Dantas was also shown the red card in stoppage time.
"We won more than a title, we managed to fight to the end and beat the leaders. Now we must rest because we have another battle ahead," said Renato, who headed Botafogo's second goal from Jobson's cross.
Fluminense notched up their eighth successive victory in all competitions but still find themselves in the relegation zone two points behind Botafogo.
Fred struck his 11th goal in 12 matches, Argentine playmaker Dario Conca also scored and an own goal by defender Ze Antonio gave "Flu" a 3-0 win away to relegated Sport Recife, who are seven points adrift at the bottom.
Fluminense, unbeaten in nine league matches, have carried their form into the Copa Sudamericana where they meet LDU Quito in the first leg of the final on Wednesday. The two teams met in the 2008 Libertadores Cup final, which the Ecuadorean side won.
