A-Rod's solo drive in the sixth off Matt Harrison (1-2) made him only the fourth player in major league history to homer both as a teenager and in his 40s, according to STATS, joining joined Ty Cobb, Rusty Staub and Gary Sheffield.
It was Rodriguez's 24th this season and 678th of his career, and it came two days after he went deep three times against Minnesota, in his previous game.
When Rodriguez was traded to the Yankees before spring training in 2004, he was only three seasons into the $252 million, 10-year contract he signed with Texas after starting his career with Seattle from 1994-2000. He got a $275 million, 10-year deal from New York after the 2007 season.
Didi Gregorius had a career-high four RBIs and matched his best with three hits, including a two-run homer in the third. His two-run single in the seventh made it 6-2.
The AL East-leading Yankees won for the seventh time in eight games, and their seven-game division lead is their largest since leading by 7 1-2 games on July 29, 2012. New York's 15-5 record in July is best in the majors.
Harrison allowed six runs and six hits in six innings in his third start since coming back from spinal fusion surgery.
The Yankees went ahead to stay when the Nos. 7-9 batters all had hits to start the third. Chase Headley singled, Gregorius homered and Brendan Ryan tripled before scoring on Chris Young's sacrifice fly.
Martin had two tremendous defensive plays in center field. He leaped with his glove near the top of the 8-foot wall to rob Mark Teixeira of a possible homer in the second, then Martin threw out Teixeira trying to score to end the eighth.
Yankees: CF Jacoby Ellsbury was out of the starting lineup with a sore shoulder a day after slamming into the wall making a catch in Minnesota. But he entered the game as a defensive replacement in the eighth.
Rangers: LHP Derek Holland is set to begin his rehab assignment Thursday with Triple-A Round Rock. It will be his first game since hurting his shoulder in the home opener April 10.
Yankees: Adam Warren or Chris Capuano will make a spot start Tuesday in place of rookie RHP Bryan Mitchell, who was in line to make the start until an accident in the weight room last week. Mitchell is OK, but hit his head after falling backward while working with exercise bands attached to a door that someone opened.
Rangers: Lefty Martin Perez (0-1, 4.91) makes his third start since returning from Tommy John surgery. The Yankees are one of only two AL opponents the 24-year-old Perez hasn't faced.