Evan Longoria followed with a double and after Carlos Pena and Matt Joyce drew walks, Dan Johnson grounded a single up the middle to chase home the decisive run, enabling the Rays to remain tied with the New York Yankees atop the American League East.
James Shields (13-11) picked up the win, allowing three runs on seven hits over 6 2/3 innings, striking out eight and walking one as the Rays took the rubber match of a three-game series at Tropicana Field.
Marco Scutaro, Daniel Nava and Yamaico Navarro drove in runs for the Red Sox.
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