The victory by the Bulls (48-16) gave them a 2 1-2 game lead over Miami for the top seed in the Eastern Conference playoffs. Chicago has two regular-season games left, against Indiana and Cleveland.
Bulls star guard Derrick Rose returned to the lineup after sitting out three games with a right foot/ankle injury and he had 11 points with eight assists in 32 minutes.
Defending NBA champion Dallas, which clinched a playoff berth on Thursday night when Houston lost, was playing the second game of a back-to-back, so veteran guards Jason Kidd and Jason Terry sat out to rest.
Deng's 3-pointer at the third-quarter buzzer capped an 11-0 run and gave the Bulls a 66-56 lead. But Dallas rallied as Vince Carter had nine points and Brandan Wright's follow-up basket cut the lead to 75-72 with just under 6 minutes remaining.
Joakim Noah and Rose scored for the Bulls before Kyle Korver hit his third 3-pointer of the game to restore the lead to nine points. Deng then hit a 3-pointer from the corner with just under 2 minutes left and Chicago had a 90-79 lead.
Nowitzki's eight second-quarter points helped the Mavs close a 13-point deficit down to six by halftime.
Hamilton had 10 points and Carlos Boozer eight as Chicago opened a 21-8 lead after one quarter -- the Mavericks' lowest scoring quarter of the season.
Notes: Rose said he just wants to get his rhythm back in the few regular-season games left. "The team is playing all right. They are playing good basketball, I'm just trying to fit in, trying to still be a part of this team and do whatever it takes to win," he said. Rose has missed 26 games this season with an assortment of injuries and Chicago is 17-9 in those games. ... Beaubois injured his left hand as he was guarding Ronnie Brewer and left the game with 7:32 left in the first half. He returned about 4 minutes later with two of his fingers taped. ... Fans cheered loudly when the public address announcer congratulated White Sox pitcher Phil Humber on his perfect game in Seattle on Saturday. The final pitch was shown on the video screen above the court.