Daniel Lynch was pitched well into the sixth inning, four relievers followed Lynch, each delivering a shutout frame, and the Royals held on for a 2-0 victory over the Twins.
The Twins have lost four of their last five on a trip through Boston and Kansas City. They also were shut out for the third time this season, matching Arizona for the most in the majors, and have not scored in their last 13 innings.
The Royals scored in the first inning when Bobby Witt Jr. grounded into a double play and Whit Merrifield scampered home from third, but nobody else crossed the plate until Kansas City strung together three singles in the fifth.
Salvador Perez got another day off from the field after treatment to drain fluid from his eye.
Royals RHP Zack Greinke (0-0, 2.45) tries again for his first win since returning to the club that drafted him two decades ago at 1:10. A day game today.