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Five players scored at least 11 points to help the Bulls (7-7) beat the Mavericks for the fourth straight time. Chicago recovered from a 93-92 loss to Milwaukee on Monday, in which it blew a 27-point third-quarter lead, largely due to the proficiency of its reserves.
"The bench was great," Thibodeau said. "The starters got us out to a good start. We needed everybody."
Nate Robinson had 14 points and a game-high six assists for Chicago, and fellow reserve Jimmy Butler scored a career-high 13, including 9-of-10 shooting from the free-throw line.
"I feel like we're coming together, getting more comfortable out there," Butler said. "They tell us all the time that you have to keep building that lead, but it definitely shows that any night, any team -- 20 down, 10 down -- they can come back and win the game."
The Bulls' bench combined for a season-high 50 points.
Joakim Noah chipped in 13 points, 10 rebounds, five assists and three blocks as Chicago avoided its first three-game losing streak at the United Center since dropping five straight in March 2010.
"It was good to come out and forget that last loss and move forward as a team," said Bulls reserve Taj Gibson, who had eight points and eight rebounds. "We understand we have a long season. There's going to be a lot of bumps in the road, but we're sticking together."
Shawn Marion scored a season-high 18 points for Dallas, which shot just 35 percent to lose for the eighth time in 11 games. The Mavericks (7-9), who had won 21 of 27 against Chicago, dropped to 2-6 on the road.
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"I loved our start to the game, but they kept chipping away and they cut the deficit, they took the lead, and our response wasn't good," coach Rick Carlisle said. "No excuses. We played last night and all that, but we just have to do a better job."
Both teams were coming off difficult losses. The Mavericks lost 100-98 at Philadelphia on Tuesday when O.J. Mayo missed a pair of free throws with 2.7 seconds left. The Bulls had a 78-51 lead in Monday's loss before the Bucks broke off a game-changing 31-4 run.
"We've got to show a collective caring for one another and a collective toughness," Carlisle said. "We're entering a really difficult stretch of our schedule. Nothing's going to be easy. We've got to embrace that challenge."
Dallas closed within six with 2:30 to go in the third Wednesday but after a timeout, Deng hit a 3-pointer and Robinson scored on a drive to give Chicago its biggest lead, 77-56.
The Bulls pushed the lead to 29 in the fourth quarter and never led by fewer than 17.
"Overall, I thought we played a lot tougher with the lead," Thibodeau said.
The crowd roared to life in the closing minutes as Chicago neared 100 points, meaning a free sandwich for everyone in attendance. Nazr Mohammed's dunk did the trick, eliciting a huge roar from the remaining fans.
Chicago's reserves keyed a second-quarter spurt to open the game. After Rodrigue Beaubois' 3 cut the lead to 31-28, Chicago went on a 13-0 run and outscored Dallas 18-2 over the next 4:40.
Dallas' leading scorer, Mayo, was held to a season-low four points on 2-for-9 shooting. He entered the game averaging 20.8 points and had scored in double digits in each of the Mavs' first 15 games. It was just the second time in his NBA career that Mayo scored four or fewer points while playing 30 or more minutes.
"Here's the thing -- we caught a break," Thibodeau said. "They're missing (Darren) Collison and Dirk (Nowitzki) and they played last night. And Mayo is dinged up with an ankle injury."
Collison was inactive because of a sprained right middle finger. The point guard has struggled recently in his first season with Dallas, shooting 35 percent over his last seven games and averaging 3.0 turnovers per contest. Collison started 14 of Dallas' first 15 games, coming off the bench for the first time this season in Saturday's loss to Philadelphia. He has been replaced in the starting lineup by third-year point guard Dominique Jones. ... Each team took the floor with its best player still rehabbing from knee surgery. Neither Chicago's Derrick Rose (left knee) nor Nowitzki (right knee), both former NBA MVPs, were at the game. ... Mayo is averaging 24.3 points on 52 percent shooting at home, but just 15.3 points on 40.6 percent shooting on the road.