Greene (3-1) followed Chris Capuano's sharp effort in Wednesday's 5-1 win with an even better performance. The rookie yielded just five singles and three walks while keeping Detroit's slumping offense off the board in the longest outing of his brief big league career.
Despite sending out a former Cy Young winner in each of the first three matchups, the Tigers dropped three of the four tests in the set, mainly due to a lineup that was held to just six runs by the Yankee arms.
Rick Porcello (13-6) was victimized by Detroit's lack of production in the finale, denied a chance at a 14th win despite scattering nine hits over seven innings of one-run ball.
Stephen Drew knocked in what turned out to be the game's only run with a ground-rule double in the fourth inning.