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.