Kuroda (8-6) allowed at least one base runner in every inning he worked and put two men on base three times, but the Twins were unable to bring home a run in what was their sixth straight loss.
Rivera struck out two in a perfect ninth for his 30th save. He had blown a save opportunity for only the second time this year in his previous outing last Sunday.
The New York runs came in the fifth on RBI singles by Brett Gardner and Robinson Cano. Those runs were charged to reliever Ryan Pressly (2-2), who came on in the fourth following a 73-minute rain delay.