With a chance to tie the major league record of four homers in a game, Granderson lined a clean single in the sixth and beat out an infield hit in the eighth. It was his first five-hit game since 2008.
Granderson homered to right-center in the first and hit a soaring, two-run shot into the second deck in right field in the second, both off starter Anthony Swarzak.
In his third at-bat, Granderson hit a line drive to the short right-field porch against Jeff Gray in the fourth for a 7-4 lead.
The Yankees held on to win 7-6.
The three-homer game was the first at new Yankee Stadium and the first for a Yankees player since Alex Rodriguez hit three at Kansas City on Aug. 14, 2010.
Lou Gehrig is the only Yankees player to hit four homers in a game, which matches the major league record.
Granderson has 13 career multihomer games. This is his first with more than two home runs.
He became the 12th major leaguer to hit three home runs in the first four innings of a game, according to STATS LLC and the SABR Home Run Log. Alfonso Soriano was the last to do it for the Chicago Cubs on June 8, 2007, against Atlanta.