Jesus Flores' first home run of the season 1, in the rubber match of a three-game series.
Flores notched his 100th career RBI with a solo shot in the fifth, while Jonny Gomes added a two-run single against his former team.
Zimmermann (8-10) worked 5 2/3 innings of shutout ball, allowing just six hits and two walks.
Drew Storen worked around a pair of ninth-inning singles to record his 33rd save of the season.
Bronson Arroyo (7-10) allowed three runs on seven hits over six innings. He walked two and struck out three and has not recorded a win since June 25.
Brandon Phillips knocked in the lone run for the Reds, who stranded 10 and went 0-for-7 with runners in scoring position.