Soriano's two-run blast in the third inning -- his first home run since returning to New York -- put the Yankees ahead 5-4. The Rays battled back for a tying run in the fifth on a solo shot by Wil Myers -- his second homer of the game.
The score remained tied until the ninth when Brett Gardner drew a leadoff walk from Jake McGee (2-3) and went to second on a wild pitch.
Jeter smacked a solo homer on the first pitch he saw in his return to the lineup after missing much of July with a strained quadricep. It was just his second game since undergoing ankle surgery last fall.
Ichiro Suzuki went 4-for-4 with an RBI for New York.
Mariano Rivera (2-2) earned the decision after tossing a scoreless top of the ninth.
Myers finished 2-for-4 with four RBI for Tampa Bay, which fell into second place in the American League East, 1/2 game behind Boston.
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