Trailing 6-4 entering the ninth and facing Indians closer Chris Perez (0-2), the Rays collected four straight hits to forge into the lead.
Will Rhymes socked a one-out homer to cut Tampa Bay's deficit to a run. Elliot Johnson then followed a single and came home when the next batter, Carlos Pena, ripped an RBI triple to tie the game.
Zobrist completed the rally with a sharp single to right field to plate Pena, and the Rays held on to take the rubber match of a three-game set at Progressive Field.
The rally made a winner of Joel Peralta (1-3) who was credited with the victory despite allowing what seemed like an insurance run for the Indians -- Shin-Soo Choo's solo homer in the eighth.
Fernando Rodney got his 25th save despite allowing a pair of hits in the bottom of the ninth.
Casey Kotchman went 3-for-5 with a bases-empty shot and three RBI for the Tribe.
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