Chicago led by 14 at halftime and 12 after three quarters, and the Bulls appeared to be headed for an easy win. But Orlando cut the lead to two with just under 3 minutes left before Chicago's Jimmy Butler jumped to intercept a pass and squelch the comeback bid.
Then, under the Bulls' basket after a Magic rebound, Butler came up with another takeaway to again foil Orlando.
It was the third win in four games for Chicago. The Magic dropped to 0-3.
Derrick Rose is still playing with a face mask as he recovers from a broken orbital bone suffered before the start of the season. He was held scoreless in the second and third quarters and finished with just six points, but had seven rebounds and a game-high eight assists. Two of his points were on free throws with 10 seconds to go that gave Chicago a 92-87 lead.
Rose missed a last-second shot that would have won the game against the Detroit Pistons on Friday night. He came into this one averaging 13.7 points a game, second-best on the Bulls behind Butler.
Butler had 12 points and five assists. Joakim Noah added nine rebounds for the Bulls.
The Magic shot just 38.9 percent on 35-of-90 shooting. They also struggled at the free-throw line, converting just 10 of 17 for 58.8 percent.
Doug McDermott came off the bench to score 12 for the Bulls.
TIP-INS: The Bulls didn't trail after taking a 17-15 lead with 5:15 to play in the first quarter. ... Orlando has connected on a 3-pointer in 659 consecutive games, dating to March 17, 2007. ... The Bulls' Kirk Hinrich sat out Sunday's game with a sore toe, but coach Fred Hoiberg said it wasn't a serious injury.
Magic: Orlando continues its three-game road trip at New Orleans on Tuesday night.