The Reds had forged a 2-1 lead on RBI from Joey Votto and Brandon Phillips earlier in the third and Bruce (3-for-5) then broke it open, golfing a 1-0 pitch over the right field fence with Votto aboard.
Phillips later added a two-run double, finishing with three RBI, and Shin-Soo Choo added solo shot for Cincinnati, which earned a four-game split against the Braves.
Lyle Ondrusek (3-0) was credited with the decision thanks to two scoreless inning in relief of ineffective starter Tony Cingrani.
Atlanta's Julio Teheran (7-5) absorbed the loss, surrendering five runs on seven hits over 5 1/3 innings.
Andrelton Simmons and Dan Uggla each socked a solo homer for the National League East-leading Braves.
Notable deaths of 2014 [PHOTOS]