Chicago moved 1 1/2 games in front of Brooklyn for the No. 4 seed in the Eastern Conference playoff race, a spot that carries with it home-court advantage in the first round.
Brooklyn took a three-point lead with 57 seconds remaining and did not score another point.
Luol Deng scored on a jumper with 44 seconds left to get the Bulls within one and Robinson's floating jump shot lifted Chicago in front.
Carlos Boozer led the Bulls with 29 points and 18 rebounds. Deng added 18 points and Jimmy Butler had 16 for Chicago.
Deron Williams scored 30 points for Brooklyn, which returned home after an eight-game road trip.