The Cavaliers had a six-point lead with 3 minutes remaining and could score only three points the rest of the way in losing their sixth straight.
Rose made a layup to give Chicago an 84-83 advantage and added a free throw after being fouled by Mo Williams. Cleveland then missed two field goal attempts before Joakim Noah hit two foul shots to give the Bulls an 87-83 cushion with 6 seconds to play.
Rose scored 29 points and had eight assists to lead the Bulls, winners of three straight. Noah and Luol Deng both had 13 points and Noah added 14 rebounds.
Cleveland, which had an eight-point lead heading into the fourth quarter, got 20 points from Antawn Jamison.