The Cardinals forged a 4-4 deadlock on Matt Adams' two-run homer in the seventh inning, and then benefited from a bizarre Miami miscue in the ninth.
After the Marlins' A.J. Ramos (3-3) had retired the first two batters of the final frame, Jay drew a walk and then took third on a single by pinch-hitter Shane Robinson. Jay scored the winning run when right fielder Giancarlo Stanton's routine throw back to the infield short-hopped first baseman Logan Morrison, going under his glove and rolling to the middle of the diamond.
Edward Mujica (1-1) was credited with the victory with a scoreless top of the ninth for the Cards, who clinched their three-game series.
Morrison belted a two-run homer and Derek Dietrich went 2-for-4 with a solo shot for the Marlins.