Simmons provided a two-run blast, a solo shot and an RBI single for the Braves, who opened a 10-game road trip with a victory.
Paul Maholm (4-3) broke a personal three-start losing streak, yielding two runs on four hits over 5 2/3 innings. The left-hander walked two and struck out six.
Craig Kimbrel was called on to record his 10th save after the Reds scored twice in the eighth inning.
Cincinnati's Bronson Arroyo (2-4) was reached for four runs on eight hits over five full frames.
Former Titans kicker dies in car crash
UPI Sports Results for September 20, 2014