The Spurs led by only two during the opening minute of the third quarter but eventually built a 15-point lead by the end of the period and coasted from there.
Bonner was one of three San Antonio players to come off the bench and reach double figures. Tiago Splitter had 16 points and Danny Green contributed 10.
The Spurs won for the ninth time in 10 home games this season.
Jeff Teague led Atlanta with 20 points. The Hawks had captured six of their previous seven.