Continuing his dominance of the Brewers this season, Straily (14-8) allowed just one run on five hits with five strikeouts over 6 2/3 innings.
The right-hander is 3-0 with a 1.67 ERA in four starts against Milwaukee in 2016.
Votto's 26th home run gave Cincinnati a 2-0 lead in the first inning against Brewers starter Taylor Jungmann (0-5).
Jungmann settled down from there, giving up just those two runs on three hits and four walks over four innings in his first start in the big leagues since April 28.
The Brewers' lone run came on Domingo Santana's homer in the second.
Scott Schebler had three hits for the Reds, while Votto and Adam Duvall each drove in two runs.