A day after C.C. Sabathia struck out nine in six innings to guide the Yankees to a 5-1 win against the Rangers, Rodriguez moved past Mark McGwire into eighth place in the all-time home run standings.
"It feels good to keep moving up the line," Rodriguez, 34, told reporters. "Long after I'm playing, I'll have a chance to reflect on that. Right now, the focus is on winning."
The surging Yankees, with Derek Jeter going 3-for-4 and A.J. Burnett pitching seven shutout innings, completed their fourth successive series win of the season.
They launched their campaign by winning two of three games against the Boston Red Sox, the Tampa Bay Rays and the Los Angeles Angels.
The last time the Yankees won their first four series in a season was in 1926.
"We just do our best to keep (the offense) in it," Burnett said. "It's only a matter of time until they explode. They did it early today."
Burnett delivered a pitching master-class with six of his seven strikeouts coming off his fastball.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Greg Stutchbury)