The Bulls took an 87-78 lead with 3:51 remaining on the last of Robinson's 19 points and they did not score again.
Orlando closed within a point when DeQuan Jones scored on a slam dunk with 1:33 to go, but both of the Magic possessions after that ended in turnovers.
Chicago trailed by five points with 10 minutes remaining, then went on an 18-4 run. Luol Deng also scored 19 points, helping the Bulls to their sixth win in eight games.
Beno Udrih had a season-best 27 points for the Magic, who have lost 12 of their last 13.