Minnesota starter Kevin Correia was dominant through seven innings.
But the Twins bullpen struggled in the eighth and lost control of the game.
After Correia held Kansas City scoreless, the Royals scored five runs off relievers Jared Burton (2-8) and Caleb Thielbar in the eighth and beat the Twins 6-1 on Tuesday night.
Burton leads the Twins with 22 holds this season, but entered the game having allowed five earned runs in six innings against the Royals.
After allowing three hits and four runs in one-third of an inning, Burton's ERA against the Royals this season had jumped to 12.79, and his record against them fell to 0-3.
''Kansas City as a whole's got our number,'' Twins pitching coach Rick Anderson said when asked about Burton's struggles against the Royals.
''I don't even know what our record against them is, I just know it's not real good. We just haven't played very well against them.''
James Shields (9-8) was sharp for 7 1-3 innings for Kansas City and Alex Gordon had...