Arroyo (6-6) won for the third time in four starts, scattering six hits over 6 2/3 innings while setting down the first 11 Rockies batters.
The right-hander didn't issue a walk and allowed only one runner to get as far as third while striking out three for National League Central-leading Cincinnati.
Alfredo Simon tossed 1 1/3 scoreless innings and Aroldis Chapman completed the shutout with his 20th save, striking out the side in the ninth.
Ryan Ludwick and Todd Frazier supplied RBI for the Reds.
Colorado's Drew Pomeranz (1-6) took the loss, surrendering three runs on seven hits over 5 1/3 frames.
Celebrity Families of 2014 [PHOTOS]