Jason Kidd had 12 points and eight rebounds, and Tyson Chandler also had 12 points for the Mavericks, who had seven double-figure scorers.
The Mavericks have won five of six after a six-game losing streak.
Joe Johnson paced Atlanta with 27 points, and Josh Smith added 17 points before fouling out with 5:41 left.
The Hawks had won 13 of their previous 17, including Friday night's 111-102 home victory over the Knicks.
For three quarters, the Mavericks couldn't prevent Johnson from getting inside. Johnson scored 18 of his first 20 points in the paint, and the Hawks led 78-77 to start the fourth quarter.
But Dallas opened the final quarter with a 14-1 run capped by Terry's 17-footer with 8:07 left for a 91-79 lead.
The Mavericks stepped up defensively down the stretch as the Hawks missed seven of their first eight field goal attempts in the final quarter.
Marvin Williams started the altercation when he shoved New York's Shawne Williams in the back as they ran up the court with 43 seconds left in the the game.
Marvin Williams will also miss the Hawks' home game against Toronto on Wednesday.
By halftime, Johnson had 16 points on 8-for-12 shooting, but Dallas finished the second quarter with a 7-0 run for a 52-49 lead at the break.
Nowitzki hit four of his five shots in the opening quarter and scored eight points as Dallas took a 28-24 advantage into the second quarter.
The Mavericks were 98-93 winners in Atlanta on Nov. 20, the only other meeting between the teams this season. Dallas has won nine of the last 12 against the Hawks.
NOTES: Marvin Williams has already missed 15 games this season with back and right knee injuries. ... F Maurice Evans moved into the starting lineup in place of Marvin Williams, who's averaging 10.9 points and 4.8 rebounds per game. ... Mavericks F Sasha Pavlovic was awaiting word after the game on his status with the team. His second 10-day contract lapsed on Saturday, and the Mavericks had to decide whether to sign him for the rest of the season or release him.