Bruce knocked in a run on a fielder's choice in the first and added his 24th home run of the season in the third that helped the Reds build a 5-1 lead.
Cincinnati starter Homer Bailey (7-10) had given up two runs and five hits through five innings and the Reds were up 6-2 but Oakland charged back with a three-run rally in the sixth.
Reliever Manny Parra came on and got the final two outs of the inning and the Cincinnati bullpen allowed two hits over 3 2/3 innings to stop the A's. Aroldis Chapman finished things with a 1-2-3 ninth for his 27th save.
The first five Cincinnati runs and seven of the Reds' 10 hits came off Bartolo Colon (14-4), who was seeking to become the second 15-game winner in the majors this season but didn't last through the third inning.
But Bruce singled in a run and added his home run in a three-run third. Corky Miller had a pair of run-scoring doubles for the Reds.
Josh Donaldson hit a home run, drove in two runs and scored twice in leading the Oakland hitters.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Costly malfunction causes beer flood at Boston-area brewery