New York moved to 5-2 on a nine-game road trip despite being outhit by the Tigers 11-9.
Derek Jeter drew a two-out walk with the bases loaded in the second and Granderson followed with his 17th homer, a shot to right off Casey Crosby (0-1).
Crosby was making his first major league start, having been called up from Class AAA Toledo to fill in for the injured Doug Fisher.
CC Sabathia (7-2) went seven innings to collect the win, giving up three runs on eight hits with five strikeouts.
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