Arroyo (6-5) rebounded from a rough outing in his previous start to dominate the Rockies on four hits. The right-hander didn't allow a walk and struck out three in the efficient, 86-pitch performance.
Aroldis Chapman recorded three strikeouts in the ninth for his 15th save as the Reds moved into sole possession of second place in the National League Central, 2 1/2 games behind St. Louis.
Bruce went 3-for-4 with a two-run shot in the eighth and Todd Frazier added an RBI for the victors.
Rockies starter Tyler Chatwood (3-1) yielded one run on four hits over four full innings before leaving with a sore triceps.