CC Sabathia earned the victory with six-plus solid innings.
Judge matched that number with a two-run shot against Royals rookie starter Jakob Junis in the bottom of the third.
As well as his homer tally, Judge has now recorded 108 RBI and 124 runs, the third best rookie total in Yankees history after Tony Lazzeri and Joe DiMaggio. McGwire set the record in 1987 as a member of the Oakland Athletics with 49 home runs.
It was his fourth multi-homer game in the last 14 contests and seventh of the season.
Also pitching in for the Yankees' win was shortstop Didi Gregorius. The two-run shot gave the Yankees a 3-0 lead.
"The way he started, I thought he was going to hit 60, 70", Yankees catcher Gary Sanchez said through a translator.
Kansas City trails the Twins by six games with six games left and headed to its final homestand before Eric Hosmer, Alcides Escobar, Lorenzo Cain and Moustakas can become free agents. He lost for the first time since June 29, giving up six runs, seven hits and striking out four in five-plus innings of work. The veteran lefty walked one and struck out four to improve to 13-5 on the year (3.84 ERA).
NEW YORK - Lucas Sims is making his case to be in the Atlanta Braves rotation next season. If the season ended today, NY would battle the Minnesota Twins for the right to play the Cleveland Indians in a first-round series. Kansas City went 37-44 on the road, three more wins than a year ago. The Royals try to bounce back on Tuesday night at 8:15 p.m.
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