Granderson homered in each of his first three at-bats, driving in four runs, and helped Phil Hughes (1-2) overcome a four-run first inning.
Mark Teixeira hit his first home run of the year and the Yankees earned a split of the four-game set. The Twins have not won a series in New York since 2001, a year before Ron Gardenhire took over as manager.
Granderson got two chances to tie the major league record of four homers in a game. In the sixth, he lined a single to right field. In the eighth, he beat out a dribbler down the first base line.
Granderson became the first big league player to hit three homers in a game this year. His first two came off starter Anthony Swarzak (0-3).
Mariano Rivera worked a perfect ninth for his third save of the season and record 606th of his career.
Derek Jeter had an RBI single for his 3,110th hit, tying him with childhood idol Dave Winfield for 18th on the career list.
In Detroit, Yu Darvish pitched two-hit ball into the seventh inning and Mike Napoli homered for the fourth straight game, leading Texas past Detroit for its seventh consecutive victory.
The Rangers beat the Tigers in six games in last year's AL championship series, winning the clincher 15-5. This one wasn't much closer, with Texas scoring five runs in the eighth and finishing with 19 hits.
Detroit (9-4) has the American League's second-best record behind the Rangers (11-2). Texas is 6-0 on the road, equaling a team record set in 1989.
Darvish (2-0) showed impressive poise in the opener of a four-game set at Comerica Park, allowing one run over 6 1-3 innings in his toughest test since coming over from Japan.
Adam Wilk (0-2) gave up two earned runs and 10 hits in four-plus innings for the Tigers.
In Toronto, Evan Longoria hit a two-run homer and came within a triple of the cycle, Desmond Jennings added a solo shot and Tampa Bay ended a 10-game road trip by beating Toronto Longoria went 3 for 4 with a season-high four RBIs and reached base four times as the Rays tagged Henderson Alvarez (0-1) for a career-high six earned runs in 6 1-3 innings.
Jeremy Hellickson (2-0) gave up three runs, two earned, in 5 2-3 innings. The Rays have won nine of their past 12 against the Blue Jays and 10 of 15 at Rogers Center.
Tampa Bay went 4-6 on a trip to Detroit, Boston and Toronto that began with seven straight day games.
In Chicago, Jason Hammel struck out 10 and closer Jim Johnson fanned Alex Rios with the bases loaded to preserve Baltimore's win over Chicago.
Adam Jones hit his fifth homer of the season and an RBI double. The two-run shot was his first this year with a runner on base.
The Orioles took three of four from Chicago and have won their first two road series of the season. Baltimore won only five road series last year.
Hammel (2-0) matched a career high for strikeouts, doing it in just six innings. He worked out of trouble early, leaving the bases loaded in the first and third.
Johnson earned his sixth save. He has converted 14 straight chances dating to last season.
Gavin Floyd (1-2) allowed five runs and six hits in six innings.
In Anaheim, California, Kurt Suzuki and Kila Ka'aihue drove in runs, Oakland scored two more on C.J. Wilson's throwing error in his home debut, and the Athletics beat struggling Los Angeles for their third straight victory.
Tommy Milone (2-1) allowed seven hits in five innings in his native Southern California to win the eighth start of his major league career as the Athletics took three of four from the big-budget Angels, who dropped to 4-9.
Albert Pujols had three doubles and missed his first homer for the Angels by just a few inches, sending a drive off the top of the left-field wall in the fifth. The $240 million man extended his hitting streak to nine games with his first three-hit game for Los Angeles, although his career-worst homer drought to open a season stretched to 13 games.
Wilson (2-1) labored through six innings of two-hit ball and Los Angeles stranded 11. Erick Aybar made two errors after receiving his Gold Glove trophy and signing his new $35 million contract before the game.
Grant Balfour earned his fourth save when Torii Hunter grounded into a game-ending double play.
In Seattle, Jack Hannahan hit a two-run single in the ninth inning off closer Brandon League and Cleveland rallied to beat Seattle, costing Mariners ace Felix Hernandez a win after his dominant outing.
Hernandez struck out 12 and walked one. He allowed five hits, three in the eighth inning, but ended up with a no-decision.
Cleveland starter Josh Tomlin (1-1) just about matched the 2010 AL Cy Young Award winner pitch for pitch. Tomlin tossed eight innings, yielding one run and five hits. He struck out seven, walked none and threw just 96 pitches.
Chris Perez got three outs for his fourth save.
Carlos Santana walked and Travis Hafner singled to open the ninth against League (0-1). Casey Kotchman's sacrifice bunt advanced both runners.
