Ryan Hanigan scored twice for the Reds, who ended a six-game road losing streak. They won for the fifth time in eight games overall.
Volquez came off the 15-day disabled list to start, but he left after the first inning because of numbness in the fingers of his pitching hand.
Mike Lincoln (1-0) pitched three innings to get the victory. Francisco Cordero got his 14th save. The Cincinnati relievers combined to allow two runs on five hits.
Colby Rasmus was 3-for-4 with a solo homer for the Cardinals.
Todd Wellemeyer (5-5) gave up four runs on five hits in five innings to take the loss.