Jimenez (1-0) held the Reds to a pair of singles in the second inning and four walks overall in 7 2/3 innings, striking out three. Brad Brach pitched the ninth for his first save, completing the two-hitter and the Orioles' first shutout of the season. The Orioles lost closer Zach Britton to a strained forearm on Sunday.
The Reds were shut out for the first time this season.
Garrett (2-1) tied the Reds' modern record for a rookie left-hander by striking out 12 in seven innings.