McCarthy (3-5) allowed six hits and two walks while fanning three in Oakland's seventh win in 11 games.
Ben Zobrist homered for the Rays' only run. Tampa Bay has lost four of its last five.
David Price (9-9) allowed four runs on seven hits over six innings.
Oakland scored single runs in the third through sixth innings to take a 4-0 advantage. After Zobrist homered in the top of the eighth, the A's tacked on a pair of insurance runs in the bottom of the eighth.
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