Rodriguez led off the seventh inning against Tampa Bay right-hander Jason Hammel with a deep drive to straightaway center field, his 30th of the season, giving the Yankees a 7-2 lead over the Rays.
The defending American League Most Valuable Player, Rodriguez has also hit 206 of his home runs as a Yankee, moving past Bill Dickey for 14th place on the franchise's all-time list.
Regarded as one of the game's great all-time third basemen, Schmidt played his entire 18-year career with the Phillies from 1972-89. A three-time National League MVP and a 12-time NL All-Star, Schmidt earned induction into the Baseball Hall of Fame in 1995.
Rodriguez is in the first year of a 10-year, $275 million contract with the Yankees that could be worth more than $300 million if he eventually surpasses all-time home run king Barry Bonds, who hit 762 with the Pirates and Giants. Next up for A-Rod would be Reggie Jackson, who is 11th with 563 home runs.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.