Bartlett connected on an offering from Kerry Wood (1-4), lining it into right center to score Carl Crawford with the winning run and boosting the Rays to their third win in a four-game set at Tropicana Field.
The victory allowed Tampa Bay to end the first half of the season with a 54-34 mark, good for second place in the American League East, 1 1/2 games behind the New York Yankees.
Austin Kearns drove in a pair of runs on two hits for Indians, who went into the break 20 games below .500 at 34-54.
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