Defeat for Chile, who pulled level at 2-2 through goals from striker Humberto Suazo, left Marcelo Bielsa's team waiting to secure a place in the 2010 finals in South Africa.
Brazil had Felipe Melo sent off in the 52nd minute for a bad foul on striker Alexis Sanchez, but Sanchez himself was shown the red card in the 77th for dissent, his second bookable offence.
They were joined by Paraguay, who made it to their fourth successive finals when they beat Diego Maradona's team 1-0 earlier on Wednesday.
The top four go through to South Africa while the fifth-placed team, at present Argentina, get a second chance in a two-leg playoff against the CONCACAF's fourth-placed team.
Nilmar, playing in the absence of the suspended Luis Fabiano and injured Robinho, opened the scoring after half an hour from Daniel Alves's cross.
"I knew this game was my chance to play, score goals and show my work ... Today we showed that the national team squad is very strong," Nilmar told reporters.
He completed his hat-trick with two goals in less than three minutes midway through the second half, both laid on by right back Maicon, after Suazo's second brought Chile level in the 52nd.
