Butler scored inside after Ellis fell down, and after two more Dallas possessions ended in misses, Hinrich hit a pull-up jumper for a 93-85 lead.
Butler blocked a layup try by Jose Calderon and made a free throw at the other end to complete the run as the Bulls outscored the Mavericks 27-15 in the fourth.
"We got nothing but good looks," said Ellis, who was 2 of 6 in the fourth and 7 of 19 for the game. "We missed a lot of layups, a lot of shots in the middle, at the free throw line. Missed a lot of wide-open ones. Just weren't going down for us."
After the Bulls went up 84-78 on back-to-back 3-pointers from D.J. Augustin and Hinrich, the Mavericks went back in front with a 7-0 run started when Nowitzki hit a one-legged fadeaway over Noah after Noah had stolen the ball from him two straight times.
Noah didn't have a point or rebound in the first half but finished with 10 points and nine boards. The team's assist leader had four more of those as the NBA's lowest-scoring team reached 100 points for the third straight game — all wins.
"We are an offensive juggernaut," coach Tom Thibodeau said with a smile. "I thought we battled back and showed more discipline as the game went along."
The Bulls took their first lead on a reverse layup by Carlos Boozer with 2:48 left in the third quarter, but didn't score the rest of the period. Shawn Marion quickly answered with a layup, and DeJuan Blair ended a 2½-minute scoreless stretch with a bucket to put Dallas up 76-73 going into the fourth.
The Mavericks made five of their first seven from long range and ran out to a 32-17 late in the first quarter, punctuated by a sprinting layup from Wayne Ellington when he was led perfectly on a long pass from Devin Harris.