Rodriguez homered for the first time since coming off the disabled list, Tanaka pitched seven shutout innings and the Yankees beat the Tampa Bay Rays 4-1 on Friday night.
"It's always good to produce and drive the ball like that," Rodriguez said of his estimated 440-foot shot.
Rodriguez returned Thursday after missing three weeks with a strained right hamstring. His sixth homer of the season and 693rd overall came off Chris Archer during a three-run sixth.
Tanaka (3-0) scattered two hits and struck out four to run his career-best unbeaten streak to 11 consecutive starts, dating to last season.
"He was unbelievable," Rodriguez said. "He was so efficient with his pitches. He could have pitched a complete game."
Carlos Beltran homered in the eighth for the Yankees, leaving him one hit shy of 2,500 for his career.
Archer (3-6) allowed four runs -- one earned -- and four hits in eight innings for the Rays, who have lost six of seven.
Brett Gardner drew a one-out walk in the sixth and went to third when Archer was charged with an error for an errant throw on a pickoff attempt. Beltran reached on an error when second baseman Taylor Motter misplayed his grounder, Brian McCann drove in Gardner with an infield grounder.
Rodriguez then hit his first homer since May 1 to center field. A-Rod, who struck out with two on and two outs in the first, is 1 for 8 since coming back.
"It was a classic example of when you play a good team, even one mistake can be costly," Archer said. "If you give a team extra outs, it's going to be costly, especially with the way Tanaka was throwing."
Rodriguez has 56 homers against Tampa Bay, including 30 at Tropicana Field.
Tanaka retired his first 12 batters before Pearce's leadoff single in the fifth. He got help to end the inning when Gardner made a leaping catch at the left-field wall on Corey Dickerson's drive.
"Maybe not as sharp as it looked," Tanaka said through an interpreter about his outing. "I think our defense played spectacularly."
Jacoby Ellsbury went 2 for 4 against Archer and has 18 hits off the Rays' opening day starter in 28 at-bats.
Yankees: Girardi didn't rule out 1B Mark Teixeira (neck) from returning Sunday or Monday. Teixeira, who sat out his third consecutive game, continued icing the injury Friday and plans to increase the treatment process Saturday.
Rays: Closer Brad Boxberger (adductor surgery) made his sixth rehab appearance Friday night with Double-A Montgomery. Tampa Bay manager Kevin Cash said the closer's status will be evaluated after the outing and that "most of it will be how he feels."
Beltran is expected to DH once this weekend because Girardi doesn't want him playing in right field all three games of the series on the artificial turf at Tropicana Field. ... Beltran had success filling in at DH while Rodriguez was on the DL, but don't look for him to get a major increase in that role "This team was built, when we started the year, for Alex to DH and Carlos to play right field," Girardi said.
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