Kuroda allowed runs in each of the first three innings, including a pair in his first inning on the mound for the Yankees.
The Yankees offense didn't fare much better against Rays starter David Price, who went six and one third strong innings, allowing just two runs.
A ninth inning rally from New York came up short, as they weren't able to overcome a six run deficit heading into the final frame. Nick Swisher connected on a three run homer to shave the margin down to 8-6, but Alex Rodriguez grounded out to end the game.
These two teams will finish out their series on Sunday afternoon, when Phil Hughes makes his season debut for New York against talented youngster Jeremy Hellickson.