The Brewers had grabbed a 5-4 lead in the sixth inning on a two-run single from Jonathan Lucroy and St. Louis went back on top in the next frame thanks to a two-run blast by David Descalso.
Milwaukee forged a 6-6 tie in the eighth on two singles and a fielder's choice grounder by Norichika Aoki.
But the Cards decided the issue in the ninth when Shane Robinson led off with a single against Jim Henderson (2-1), went to second on an error by Brewers center fielder Carlos Gomez, stole third and came home on Jay's hit.
Jay also slammed a three-run homer, finishing with four RBI, and Allen Craig added a bases-empty homer.
Seth Maness (1-0) earned his first major league victory and Edward Mujica notched his eighth save as St. Louis took a third straight from Milwaukee.
Jean Segura clubbed a two-run homer and Gomez went 2-for-4 with solo shot for the Brewers.