With the score tied 4-4 in the 10th, the Cardinals grabbed the lead with one out when David Descalso stroked a wind-blown RBI double against J.J. Hoover (0-5).
Two batters later Matt Carpenter (three RBI) made it 7-4 with a two-run, broken-bat single.
After Carlos Beltran drew a walk to load the bases, rookie pitcher Curtis Partch made his major-league debut and Holliday hammered his first pitch 464 feet to left-center for his fifth career grand slam.
Beltran clouted a solo homer and finished with two RBI for the National League Central-leading Cardinals, who took two-of-three from Cincinnati.
Trevor Rosenthal (1-0) notched his first big-league victory with two scoreless innings of relief.
Jay Bruce went 2-for-3 with three RBI for the Reds.