The Pistons trailed in their home opener by nine points entering the fourth, but dominated the first 11 minutes of the final period before a late Hawks rally.
Two 3-pointers by Joe Johnson pulled Atlanta to 89-88 with 40 seconds to go, but Jarvis Hayes grabbed a key offensive rebound and Billups made it a 3-point game from the line.
Rasheed Wallace then fouled Josh Smith on a desperate 3-point attempt, and Smith hit all three free throws to make it 91-91 with 7.7 seconds left.
Billups was fouled by Marvin Williams on a drive to the basket, and hit the first free throw. He missed the second, but Atlanta couldn't get a shot off before the buzzer.
Billups finished with 22 points and Richard Hamilton added 21 in his season debut. Jason Maxiell added 15 points and eight rebounds for Detroit, which overcame three starters scoring in single digits to improve to 3-0.
NOTES: Hamilton missed the first two games of the season while attending the birth of his son. ... Pistons G Flip Murray made a fourth-quarter free throw despite the distraction of a steam cannon going off behind the basket as he was shooting. The device had been used moments earlier during a performance by the Detroit dance team.