Kris Medlen and three relievers combined on a six-hitter as Royals dropped the Indians, 2-0, at Progressive Field.
Medlen tossed six-and-a-third innings of scoreless ball to earn his fourth win. Greg Holland earned his 31st save.
Alex Rios had a solo shot, and Salvador Perez added an RBI single as Kansas City snapped a two-game skid.
Josh Tomlin struck out six, but allowed but runs to fall to 5-and-2 with the complete-game loss. Cleveland was 0-for-7 with runners in scoring position.