Bailey (5-3) allowed two runs on five hits, fanning six and walking one over seven effective innings. Three relievers finished off the victory, inclduing Aroldis Chapman, who struck out two in a perfect ninth to earn his fifth save.
Brandon Phillips hit a two-run homer for the Reds, who avoided a sweep and put the brakes on a four-game losing skid.
Clayton Kershaw (3-2) was charged with seven hits and three runs despite striking out nine over seven full frames for the Dodgers, who had won three straight. Yasiel Puig launched a solo homer in defeat.