Rodriguez drove in the New York Yankees' fifth run of the game in an 8-7 win over the Los Angeles Angels at Yankee Stadium with a single to right, driving in Brett Gardner, who had tripled into the left-center gap.
It was A-Rod's 1,997th RBI, breaking a tie with Bonds he established May 28 with a sacrifice fly in a 5-4 loss to the Athletics in Oakland.
Aaron is baseball's RBI leader with 2,297.
"It just means I'm getting older, every day," he said. "I'm happy. I'm in a good place. It doesn't escape me that all these milestones are coming at home in front of our fans. The fans for me have been a huge part of this. They've welcomed me from day one in Tampa and New York, and made me feel very comfortable.''
Added Yankees manager Joe Girardi: "It's amazing, just because of the names, the people that he's passing. These are all incredible players, and like I said, there's a lot of years that he's been extremely productive and he's being productive again."