Tony Pena Jr. added two hits and two runs, and Shane Costa scored twice for the Royals.
Odalis Perez (3-5) won for the first time in his last seven starts, allowing eight hits and four runs in five-plus innings.
Brendan Harris hit a three-run homer for the Devil Rays.
Winless Edwin Jackson (0-7) allowed six hits and six runs over 3 1/3 innings, as his ERA rose to 7.77 on the year.
Celebrity Breakups and divorces of 2014 [PHOTOS]