Cobb (9-8) issued only four hits and a walk while striking out five over seven innings for the Rays, who clinched their three-game series and pulled to within 1 1/2 games of the Yankees and the Baltimore Orioles atop the American League East.
Longoria's blast in the third inning erased a 2-1 deficit and put Tampa Bay ahead for good.
Desmond Jennings and B.J. Upton added back-to-back solo shots in the fifth.
Freddie Garcia (7-6) was touched for five runs on five hits over 5 1/3 innings as New York lost for the 11th time in 12 games at Tampa Bay.
Robinson Cano belted a two-run homer for the Yankees. who surrendered sole possession of first place in the AL East after holding it for 84 days.
Aaron Carter is still in love with Hilary Duff
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