"It's definitely not the result I wanted but we've just got to keep fighting," Noah said. "We've got to come with a better edge."
Derrick Rose scored 19 of his 32 points in the fourth quarter and added 10 assists, and Carlos Boozer had 24 points for the Bulls, who had won 10 of their previous 12.
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Amir Johnson scored 17 points, Leandro Barbosa had 13 and Sonny Weems 12 as the Raptors beat the Bulls for the first time in three meetings. Toronto had won just two of its past 20 but shot 58.1 percent against the Bulls, the best showing by a Chicago opponent this season.
Asked what disappointed him most about his team's defense, Chicago coach Tom Thibodeau was blunt.
"What didn't?" he said. "Every aspect. Start with defensive transition, keeping the ball out of the paint, challenging shots. Every aspect of our defense went out the window."
"Offensively we scored more, but defensively it was a disaster," Thibodeau said.
The Bulls, who host the Heat on Thursday night, don't have much time to sort out what went wrong.
"We wanted this so we would go into [the Miami game] with a lot of confidence," Rose said. "Now we've got to go into it very aggressively. We've got to prove the point that we can play defense."
Noah returned to the starting lineup after missing 30 games because of surgery to repair a torn ligament in his right thumb. The Bulls had gone 22-8 in his absence.
Thibodeau said he would use Noah in 6- to 8-minute increments as he worked to regain his conditioning. Noah finished with seven points and had 16 rebounds in 24 minutes.
"He missed a lot of time," Thibodeau said. "He's rusty. His timing is not there."
After Brewer missed a free throw that would have tied the game at 92 with 8:27 left, Toronto answered with a pair from the line by Weems, a baseline jumper from Barbosa and an alley-oop pass from Calderon to Johnson, forcing the Bulls to call timeout with 6:14 left and the Raptors up 98-91. Rose stopped the run with a three-point play before Toronto pushed its lead to eight.
Boozer scored on a layup and a hook shot as the Bulls scored six of the next eight points, making it 104-100 with 3:04 remaining. Barbosa's three-point play gave Toronto a seven-point lead, but Rose made four straight free throws, then tied the game at 107 on a 3 with 1:59 left.
DeRozan and Rose each made layups, then each made a pair from the line. DeRozan made two more free throws with 49 seconds left and, after Rose missed a jumper at the other end, a layup by Johnson gave the Raptors a 115-111 lead with 16 seconds to play.
"Defensively we just weren't there," Rose said. "When we needed a stop toward the end."
Noah missed all four shots he took in the first quarter but did pick up 10 rebounds, and Deng scored 10 points as the Bulls led 27-21 after one quarter. The Raptors battled back to tie it at 43-all late in the first half, but the Bulls reclaimed the lead thanks to seven points from Boozer. An alley-oop from Calderon to DeRozan cut Chicago's lead to 58-55 at the half.
Toronto led 81-72 on a jump shot by Davis with 2:37 left in the third but the Bulls ended the quarter with a 9-4 run to trail 85-81 heading into the fourth.
Acquired from the Bulls on Monday in exchange for a first-round draft pick in 2011, James Johnson made his first start of the year against his former team. He finished with nine points.
"From the opening tip he brought an aggressiveness that we wanted him to bring," Raptors coach Jay Triano said. "He had three blocked shots and he likes to get up."
Philadelphia shot 56.3 percent against Chicago on Jan. 7, beating the Bulls 105-99. ... Chicago is 13-13 on the road. ... Before the game, James Johnson spoke about the trade giving him a "fresh start" and explained how he chose his new jersey number, zero. "I wanted to start from zero and work my way up," he said. ... Calderon topped 10 assists for the sixth straight game, a career-high.
From Elias: For the third time this season, the Toronto Raptors did not make a 3-pointer. (They were 0-5 from the 3-point line on Wednesday against the Bulls.) Earlier this season their streak of 986 consecutive games with a made three-pointer came to an end.
Wednesday marks only the second time in franchise history that the Raptors won a game in which they did not make a 3-pointer. The other instance was Nov. 4, 1997. That day, they went 0-for-7 behind the arc in a 104-86 win over the Golden State Warriors. Three players on that Raptors' team are still in the NBA: Chauncey Billups, Tracy McGrady and Marcus Camby.