With the game tied 2-2 and Chicago's Ramon Troncoso (1-3) on the mound, Giambi came up to hit for Mark Reynolds leading off the frame and sent a pitch deep over the center-field fence for a walk-off game-winner.
The late clout made a winner of Chris Perez (3-1) who had tossed a scoreless top of the ninth as the Indians reeled off a fifth straight triumph.
Tribe starter Zach McAllister tossed seven innings of two-run ball while White Sox counterpart John Danks also yielded two runs over six full frames.
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