"I've learned in my career that it's always better to be remembered for some of the good things you do on the field -- and good for him," Rodriguez told reporters before playing the Red Sox. "He threw a perfect game. And, even better, he beat the Rays."
Rodriguez had drawn Braden's ire during an April 22 game when he jogged over the pitcher's mound on his way back to first base after a foul ball. Braden reportedly told the third baseman, "This is my mound, my rubber." He was irked that Rodriguez had broken one of baseball's unwritten rules, about opponents staying off the mound.
After that game Rodriguez took a jab at the 26-year-old lefty, who had only 17 career wins.
"He told me to get off the mound," Rodriguez said. "I was a little surprised because I never heard that, especially from a guy with a handful of wins in his career."
Braden returned fire, saying, "If my grandmother ran across the mound she would hear the same thing he heard. Those guys, from top to bottom, it's a classy organization. From top to bottom they do it right. [Rodriguez] should maybe just watch his captain [Derek Jeter] a little more often. It doesn't start and end with him over there at third."
Braden escalated his comments in a television interview last week.
"He's an individualistic player," Braden told Comcast SportsNet. "He plays for the name on the back of the jersey, not the front. I don't know if he's noticed, but he doesn't have a name on the back over there, so he should play for the name on the front."
Before Sunday night's Boston-New York game, Yankees manager Joe Girardi was asked about Braden's run at history, which at the time was entering the eighth inning.
"I hope he gets it," Girardi said. "I don't have any hard feelings toward Dallas Braden."
JOE POSNANSKI: UNHERALDED BRADEN MAKING US BELIEVEGAME RECAP: BRADEN PERFECT IN 4-0 WIN OVER RAYS