The 39-year-old drove a 0-1 slider from Chris Young (4-1) over the left field wall, bringing up 1,995 RBIs to take him past Hall of Famer Lou Gehrig.
Michael Pineda (6-2) rebounded from consecutive losses and Brian McCann hit a solo shot for the Yankees, who completed a three-game sweep of the Royals
A-Rod also brought up his 665th home run and 2,880th hit, leaving him 20 shy of joining Derek Jeter as the only Yankee to reach 3,000 hits.
He then added his 2,881st hit with a single in the seventh and finished the game one behind Barry Bonds, who is well adrift of Hank Aaron (2,297).
Chris Young (4-1) gave up both of New York’s home runs as the Royals slipped to a fourth consecutive defeat.