Robinson's late production highlighted run that saw the injury-depleted Bulls score the game's final 10 points to shock the top-seeded Heat in the opener of their Eastern Conference semifinal series.
The Chicago point guard contributed nine assists while Jimmy Butler -- filling in for the injured Luol Deng -- provided 21 points and 14 rebounds in the victory.
Joakim Noah shook off a foot injury to supply 13 points, 11 boards and four assists while Marco Belinelli (10 points, seven rebounds) hit game-tying 3-pointer with 1:59 remaining to ignite the decisive surge.
LeBron James supplied 24 points, eight rebounds and seven assists for Miami, which shot just 39.7 percent from the field in the face of Chicago's tough defense.
Dwyane Wade, returning to the lineup after sitting out the Heat's last game with sore right knee, was limited to 14 points.