The Bulls built a nine-point cushion at halftime but scored just 12 in the third quarter as the Mavericks seized a 60-56 lead.
Derrick Rose's layup for Chicago with 8:54 remaining tied the score at 66-66 and C.J. Watson sandwiched a Jason Terry basket for Dallas with a pair of three-pointers to open up a 72-68 lead that the Bulls would not relinquish.
A win is a win, Rose said. Everything that went on in that game was kind of terrible, except the way we played defense.
Rose led all scorers with 26 points and had nine assists, while Kurt Thomas had nine points and 11 rebounds for Chicago.
I know I can shoot, said Thomas. I just do what's asked to help this team win. Play solid defense, rebound and when the shot is there, shoot it.
For Dallas, Dirk Nowitzki top scored with 19 and Tyson Chandler recorded a double-double with 12 points and 12 rebounds. Terry scored seven of his 12 points in the fourth quarter but missed a three-pointer that would have tied the game with 16 seconds left.
Chicago's Kyle Korver hit a pair of free throws with five seconds left to ice the win.
Their team finds ways to win, Mavericks coach Rick Carlisle said. That has kind of defined their season.