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The Bulls rallied from a 13-point deficit to tie the score 78-all with 9:27 remaining on Butler's dunk after a steal. Robinson then fed Deng for a layup and an 80-78 lead, Chicago's first advantage since 1-0.
The Bulls came up with four of their 10 steals in the fourth quarter, including three by Butler.
"We dodged a bullet," Bulls coach Tom Thibodeau said. "We were fortunate, got out of a hole. ... We were just trying to find a way in the end. I thought it was the hustle plays."
Deng and Robinson each hit 3-pointers to extend the Bulls' lead to 91-84. Stuckey's layup cut Chicago's lead to one with 1:27 left before Deng had a layup for a 94-91 lead. Charlie Villanueva missed a 3 with 5.9 seconds left and Daequan Cook made a free throw.
Stuckey made a 3 before the buzzer for the final margin.
Butler bounced back from a disappointing game after he scored four points on 1-of-8 shooting in Saturday's 100-98 loss to Dallas.
"It was tough. After 2 to 3 hours of sleep, I got here super early to shoot some free throws and some jumpers," Butler said. "I don't want to play like that. Nobody wants to play like that."
Chicago also rallied from 17-point deficits in each of its two previous games against Detroit this season. The Pistons last defeated the Bulls at the United Center on Feb. 24, 2006.
"We haven't won too many against them," Monroe said. "You want to end that streak. But we want to get any win right now versus any team."
Detroit shot 50 percent (36 for 72) from the field while the Bulls shot 40 percent (30 for 76).
"We had some possessions on both ends you'd like to have back," Pistons coach Lawrence Frank said. "But if we'll give ourselves a chance, it's a whole different spirit and intent compared to the way we played against Minnesota and Toronto. We have eight more opportunities to grow as a group."
The Pistons jumped out to leads of 9-1 and 18-5, and led 24-20 after the first quarter. Cook hit a 3-pointer and a free throw with 15.5 seconds left before halftime to cut Detroit's lead to 55-53.
Stuckey made a running jumper with 2.8 seconds left to put the Pistons up four at the break.
Detroit shot 60 percent from the field in the first half, while the Bulls were at 43 percent. Stuckey led the Pistons with 16 points and Deng led Chicago with 12.
Chicago also struggled with free throws, missing 13 of 40.
Villanueva had 14 and Jose Calderon added 11 for the Pistons, who went 1-13 in March.
"We definitely got better as far as not having a big lapse that pretty much cost us a game," Monroe said. "We have to take tonight -- there were a lot of good things even though we lost -- and build up and get ready for Toronto tomorrow."
Robinson and Pistons forward Kyle Singler each received technical fouls and Pistons guard Brandon Knight was called for a flagrant foul with 2:32 remaining in the first quarter after Knight was called for a travel and raised his arm, hitting Butler in the face. Robinson then appeared to push Knight, and Singler and other players joined the fray before the players were separated. Butler made both free throws to cut Detroit's lead to 24-15.
Butler said he thought Knight's contact was unintentional. Robinson said he'll stick up for his teammates.
"I got my guy's back regardless," Robinson said. "I'm not really worried about technical or whatever."
Joakim Noah and Marco Belinelli sat out for the Bulls. Noah has missed five straight games for plantar fasciitis in his right foot, and Belinelli has sat out four games with a strained abdominal muscle. Thibodeau said both players are day to day. Noah had career highs of 30 points and 23 rebounds against Detroit on Dec. 7.
Chicago went 7-7 in March.
- The NBA upgraded Gibson's shooting foul against LeBron James in the Bulls' 101-97 victory over the Miami Heat on Wednesday to a flagrant foul, according to the South Florida Sun Sentinel. The victory snapped Miami's 27-game winning streak, the second longest in NBA history. "I guess we have to call the league and get clarification," Thibodeau said. "I didn't see it that way. I still don't have a good understanding of what a flagrant foul is. I thought I got some clarity last year, but apparently I didn't."
- Calderon has a tendon problem in his arm that flared up, affecting his shooting, Frank said.
- Knight returned for the Pistons from an ankle injury he suffered Friday.