Palmeiras opened a two-point lead over title holders Sao Paulo, who beat fourth-placed Internacional 1-0 on Wednesday, after Atletico Mineiro were upset 2-1 by bottom team Fluminense.
With six matches to go, Palmeiras have 57 points, Sao Paulo 55, Mineiro 53 and Inter 52.
He then converted a penalty in the 75th minute and completed his hat-trick three minutes from time. The striker also laid on his team's third goal for substitute Deivid Saccony.
"It was a marvellous night. I hadn't been playing well in our last matches but I was confident of my potential," Obina said.
"Tonight I can put my head on my pillow and sleep peacefully," added Obina, who was given a standing ovation when he was substituted near the end.
Both teams are level with 51 points in the race to get into the top four and secure a place in next year's South American Libertadores Cup.
"Barueri didn't do anything wrong, we didn't allow Flamengo to win the match, we tried to win ... There can't be a punishment for a team that do their duty and show professionalism," Baiano told reporters.
