Kuroda, 37, got the loss after giving up six runs (four earned) off of eight hits and four walks in five and two third innings.
Relieving Kuroda was lefty-specialist Clay Rapada, who got the final out in the sixth inning and the first out of the seventh, but also gave up two hits, two walks, and two runs.
Cory Wade came in for Rapada in the seventh inning and finished the game for the Yankees, pitching a perfect inning and two thirds with three strike outs.
After being down 4-0 early, the Yankees rallied for two runs in the fourth inning to cut the lead down to 4-2. Andruw Jones and Eduardo Nunez each had an RBI single.
Down 8-2 in the ninth inning, Raul Ibanez hit a pinch-hit sacrifice fly to score Curtis Granderson and Nick Swisher hit a three run home run to make it 8-6. However, the Yankees couldn't complete the comeback after Alex Rodriguez grounded out with Robinson Cano on base to end the game.
The Yankees lineup totaled for nine hits and seven walks, but couldn't score enough runs to make up for the poor pitching performance in Kuroda's pinstripe debut.
New York (0-2) will play Tampa Bay (2-0) at 1:40 PM ET on Sunday to complete their first series of the regular season. Phil Hughes will start for the Yankees and Jeremy Hellickson will get the start for the Rays.
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