Each blast also proved historic for the 6-7 right fielder.
That means Judge now owns the all-time single-season rookie home run record.
McGwire hit 49 homers for Oakland in 1987, breaking the previous mark of 38 set by the Boston Braves' Wally Berger in 1930 and matched by Cincinnati's Frank Robinson in 1956.
New York Yankees right fielder Aaron Judge hit two home runs Monday to set the record for most in a season by a rookie. Former Athletics pitcher Trevor Cahill coughed up Judge's record-breaker - a solo shot in the seventh inning to put the Yankees up, 7-3.
BTS sets record on Billboard 200 chart with new album
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Judge looked like he'd break this record easily by the All-Star break, but he had a terrible second half through August.
The 23-year-old hit 30 home runs before the All-Star break and then plumetted to earth, striking out in a record 37 consecutive games.
The Royals (76-79) are six games behind the Minnesota Twins in the race for the second American League wild-card spot.
The former Fresno State talent is 2-for-4 on Monday with two home runs - with the other coming in the third inning of Kansas City starter Jake Junis.