Junior Digao and Rafael Sobis looked to have put Fluminense in command, but Dos Santos Aloisio and Joao Paulo gave the home side a point.
Figueirense are one point adrift at the foot of the table, while Fluminense are level on points and goal difference with leaders Atletico Mineiro, albeit having played two games more.
Elsewhere, Vasco da Gama beat Portuguesa 2-0 in a game which saw both sides finish with ten men. Felisbino Alecsandro put Vasco da Gama in front on 37 minutes and the visitors then had Valdomiro sent off just three minutes later.
Carlos Tenorio doubled the home side's lead just after half-time and the dismissal of Henrique Pipico ten minutes from the end had no effect on the outcome.
In the day's final game, Gremio drew 0-0 away to Palmeiras despite having Kleber sent off after just 19 minutes.