Rodriguez's 18th home run of the season came in the second inning against Boston knuckleballer Tim Wakefield. A-Rod took a curtain call after circling the bases.
Next up for the 32-year-old Rodriguez is Mike Schmidt, who finished with 548 homers.
Mantle hit all of his homers for the Yankees in a career that began in 1951 and ended in 1968. Rodriguez has 191 homers since joining the Yankees in 2004.
The Yankees beat the Red Sox 5-4 in 10 innings.
Information from The Associated Press contributed to this report.