Cruz's outburst came just 10 days after he smacked three homers in a game against the Chicago White Sox.
Cruz, who notched his fourth game of the season with five runs-batted-in, got the ball rolling with a two-run homer to the opposite field in the first inning that put the Twins up 2-0.
One inning later he belted a 466-foot shot to left center field.
His third homer of the night came in the sixth inning, when he deposited a pitch from Royals reliever Jorge Lopez into the right field bleachers.
Cruz now has 11 homers and 23 runs-batted-in his last nine starts.
The 39-year-old became the first player in Twins history to have multiple three-homer games in a Major League Baseball season.