Kennedy, who was signed to a five-year deal this offseason, worked 6 2/3 scoreless innings, giving up five hits while walking one and striking out seven.
Left-hander Tommy Milone started for the Twins, who lost their fifth straight, and was perfect for three innings. But after giving up two homers in the fourth, he was let down by his defense in the fifth when shortstop Eduardo Escobar committed two errors, leading to two unearned runs.
Chien-Ming Wang pitched a scoreless ninth for the Royals, his first Major League appearance since 2013.