The score had been tied 1-1 since the third inning when the Rays finally broke through was a run in the 10th against Giants reliever Jean Machi (2-1).
With the Giants outfield playing in, Myers sent a fly ball over the head of left fielder Jeff Francoeur to push Jennings home with the game-winner.
Zobrist got the other RBI for second-place Tampa Bay, which stayed one game behind Boston in the American League East.
San Francisco's Tim Lincecum threw seven innings of one-run ball but was saddled with a no-decision.
Brandon Crawford got the Giants' only RBI.
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