Atlanta shot 36 percent from the field and Dallas wasn't much better at 37.3 percent.
Atlanta Coach Mike Woodson credited the Hawks' defense with holding Dallas off, particularly in the fourth quarter as Atlanta outscored Dallas 16-15.
"It was one of those knockdown, drag-out games, and we were just fortunate that we came out on top," said Woodson, whose team came to Texas after a loss to the Knicks Friday.
Atlanta went on a 10-1 run in the fourth quarter to break open a tie game and take a 74-65 lead. Dallas got to within three with 40.4 seconds to play but could not close the gap further.