Lowe (3-1), who was dealt to the Indians from Atlanta following the 2011 season, scattered eight hits while issuing one walk and striking out five.
Chris Perez earned his seventh save despite yielding a run in the ninth as the Indians won for the eighth time in 10 contests.
Jonathan Sanchez (1-1) was tagged for four runs on four hits over 4 2/3 innings as the Royals fell for the 12th straight game.
Mitch Meier went 3-for-4 with a two-run double for Kansas City.
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