The Boston Red Sox also lost, so the Rays stayed two behind Boston in the AL Wild Card race.
Granderson keyed a four-run Yankees second inning with a three-run double down the right-field line. He drove in another run on an infield single in the fifth.
The Rays managed just six hits in 7.2 against Nova, all of them singles. He struck out three and walked three. The Rays' best chance at scoring came in the seventh, when they loaded the bases with no outs, but Nova got Desmond Jennings to fly out and B.J. Upton to ground into a double play to end the threat.
Wade Davis took the loss for the Rays, allowing five runs and five walks in 4.2 innings.
The Yankees and Rays play six more times down the stretch, including a doubleheader on Wednesday. If the Yankees can win any one of those games, they will clinch a playoff spot. The Red Sox are six games back of the Yankees, and the Rays are eight games back.