"Finally," said Spurs guard Tony Parker. "It was a big win for the team and our confidence and to prepare ourselves for the playoffs."
The victory allows the league leading Spurs (59-19) to maintain their grip on home court advantage throughout the playoffs.
They remain 1-1/2 games ahead of the Eastern Conference leading Chicago Bulls, who beat the Phoenix Suns 97-94.
Manu Ginobili scored 12 of his 18 points in the fourth quarter to lead the Spurs, who held a one point advantage at the end of the third quarter.
Atlanta seized control of a see-sawing first quarter with an 11-2 run late in the period.
They built an 11-point lead in the second quarter but the Spurs pushed back with a 12-4 run at the end of the period to narrow Atlanta's lead to 46-43 at halftime.
San Antonio completed the comeback and took the lead on two free throws by Parker in the third quarter. Atlanta briefly regained the lead but Parker put the Spurs ahead for good with a short jump shot with four minutes left in the third.
"I think they picked up the tempo a little bit and it took us out of some things we wanted to run and how we wanted to do it," said Hawks center Al Horford.
"They're just a great defensive team. They have a lot of guards that just keep attacking you in different ways."
Parker led the Spurs with 26 points while Tim Duncan added 17 points. Joe Johnson led the Hawks with 21 points and Jamal Crawford scored 20 points off the bench.