The Mariners had taken a 2-1 lead in the top of the 11th when Jesus Montero slammed a solo homer off Wade Davis, but the Rays rallied in the bottom of the frame.
After the Rays' J.P. Howell (1-0) pitched a scoreless top of the 12th, Ben Zobrist drew a one-out walk, went to second on a Carlos Pena single and scored when Johnson sliced a hit to left field, beating the tag at the plate from catcher Montero.
The red-hot Rays won for the eighth time in nine games.
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