Milone (4-5) posted his first victory since April 15, breaking a five-start losing streak. The left-hander allowed five hits and three walks while striking out four.
Ryan Cook and Sean Doolittle each tossed a scoreless relief frame and Grant Balfour finished up with his eighth save as the Athletics clinched their three-game series.
Trailing 1-0 since the first inning, the A's broke through with a pair of runs in the sixth.
One out later, Moss sent Crisp home with a three-bagger.
Santana (3-3) allowed two runs on four hits over seven full frames for Kansas City.
Billy Butler drove in the Royals' only run.
Celebrity Families of 2014 [PHOTOS]