The Red Sox have a magic number of one to clinch the American League East, while the Yankees sit four games back of the second AL Wild Card spot.
With Boston hoping to clinch the division on rival turf, AL Rookie of the Year Award candidate Gary Sanchez spoiled the Red Sox's fun quickly with his 20th homer, a two-run shot.
Jacoby Ellsbury hit an RBI single in the fifth and Didi Gregorius added a solo homer, his 20th, in the sixth. Price surrendered 12 hits to tie his season high; in four starts against New York this season, the lefty is 1-3 with a 7.