De La Rosa (3-3) allowed three hits and struck out two before stepping aside for a trio of relievers who each pitched a scoreless inning, including Rafael Betancourt, who gave up a leadoff single in the ninth but then closed the door for his ninth save.
The win got the week off to a good start for the Rockies, who lost two of three to Tampa Bay over the weekend.
Kuroda was otherwise solid for the Yanks, who have lost three of their last four games. Kuroda gave up seven hits and struck out three over seven innings. Jayson Nix had two of the Yankees' four hits.