The Royals pushed across three runs in the fifth inning to take a 4-1 lead. Jeff Francoeur, Mike Moustakas and Brayan Pana each singled home a run.
Josh Tomlin (1-2) took the loss after surrendering four runs on eight hits in four and 2/3 innings. Luis Mendoza was the winning pitcher for Kansas City, going five innings and allowing two runs. Jonathan Broxton pitched a scoreless ninth inning for his second save of the season.
Jason Kipnis had two hits and walk for the Indians, while Michael Brantley and Asdrubal Cabrera each had a hit of their own.