Teixeira's leadoff homer to left field off Randy Wolf in the third inning was the 300th of his career, giving the Yankees a 3-0 lead.
The 300 home runs are the most by a switch-hitter through his first nine Major League seasons. Yankees icon Mickey Mantle is second with 280.
"It's not a big milestone," Teixeira said. "I'm not trying to downplay it, but it's not 500 or 600 or anything like that. For me, I just try to go up there and swing the bat hard and try to hit something."
Teixeira has done just that, hitting four home runs in his past five games.
Teixeira was able to retrieve the ball from the fan who caught it, promising the fan a trip to batting practice, along with a signed ball and bat.
"I have each one of 100, 200, 300," Teixeira said. "Those are always fun to keep in my office and break them out every now and then."