The Cards fell behind 4-2 in the fourth inning but used RBI singles from Carlos Beltran (3-for-5) in each of the fifth and seventh frames to forge a 4-4 deadlock.
Then in the eighth, Yadier Molina collected a one-out single against Michael Bowden (1-2), went to second on a wild pitch and came home with the decisive score when Jay lined a solid hit into right-center field.
The comeback made a winner of Seth Maness (2-0), appearing in just his third major league game, who tossed 1 2/3 shutout innings in relief of starter Jake Westbrook.
Nate Schierholtz drove in two runs and Anthony Rizzo went 3-for-4 with a run scored for the Cubs.
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