Bailey (2-3) struck out 10 Floridians in the win and Xavier Paul provided the firepower with a bases-clearing double in the five-run Cincinnati second inning.
The Reds took control early and led 6-1 after two innings. Ricky Nolasco (2-5) was roughed up in his start for the Marlins and took the loss with six runs on seven hits and two walks over five innings.
Derek Dietrich went 2-for-4 with an RBI for Miami. Rob Brantley drove in the other run for the Marlins.