Kurt Thomas added nine points and 11 rebounds, while Luol Deng grabbed 12 rebounds with seven points for the Bulls, who played their third straight contest without forward Carlos Boozer.
Boozer has missed the team’s last three games as he recovers from a sprained left ankle he suffered in Chicago’s 99-96 victory over Miami on Saturday.
Dirk Nowitzki paced the Mavericks with 19 points, while Tyson Chandler, DeShawn Stevenson and Jason Terry each contributed 12 points. The Mavericks have lost seven of eight dating back to January 6.
The Mavericks took a 60-56 lead into the fourth quarter, however, after a Rose reverse layup with just inside nine minutes remaining, the game was tied a 66-66.
C.J. Watson then connected on a three-pointer to give Chicago a 69-66 advantage, and the teams traded baskets into the final minutes.
Thomas hit on a mid-range jumper with 3 1/2 remaining to put Chicago up 78-73, but Nowitzki responded with a 4-0 run of his own, capped by an 18-foot fadeaway jumper at 2:14 to trim Dallas’ deficit to 78-77.
After Nowitzki failed to extend the run with a missed jumper, Rose sank a short basket with 55 seconds left to extend the Bulls lead to 80-77.
Terry missed a chance to even the game on a three, and after Chicago called a timeout, Kyle Korver made two foul shots to seal the game with 5.5 seconds remaining.
Dallas took a 20-19 lead after the first quarter, and the Chicago bench led the way in the second, scoring 18 of the Bulls’ 25 points as they took a 44-35 lead into the break.
The Mavericks opened the third quarter with a 15-4 run, capped by a Stevenson three-pointer, to take a 50-48 lead just inside seven minutes.
After Taj Gibson evened the game with a jumper at the far end, the teams traded baskets down the stretch. Brendan Haywood ended the quarter with a layup, and Dallas had a 60-56 advantage entering the fourth.
Korver scored nine points while both Watson and Ronnie Brewer added eight points to lead the Chicago bench…Deng’s 12 rebounds were a season- high…The Bulls held a 51-41 rebounding margin, and 28-16 advantage in points in the paint.