Kuroda pitched well and deep into the game. After throwing a splitter in the seventh that got away from catcher Russell Martin, Nick Markakis broke from third base to capitalize on the error, but Kuroda got to the plate in time, catching the ball from Martin and getting the tag on Markakis.
The Yankees were able to hold onto their 2-1 lead after that with the help of setup man David Robertson and closer Mariano Rivera.
Eric Chavez smashed a two-run home run in the second inning, giving Kuroda the run support to get his second win at Yankee Stadium this season.
Kuroda had a strong outing on the mound throwing 87 pitches, 52 for strikes. Monday's game lowered his ERA to 3.69.
"I thought he pitched effectively inside," said Yankees manager Joe Girardi, who was impressed with Kuroda's performance.
"I thought his slider was good tonight. The only walk that he had scored. He attacked the zone all night, and I thought he was effective."
Kuroda has had a bit of difficulty this season. His record for the 2012 season currently stands at 2-3.
Monday's game versus the O's showed that Kuroda has the capability of having a strong, solid outing in a tough place to pitch like Yankee Stadium. His win should be a good boost for his confidence coming off a few letdown performances.