Milone (9-8) yielded four hits and worked around four walks. The left-hander struck out six and got some defensive help from a sixth-inning double play.
Ryan Cook hurled a scoreless eighth and Grant Balfour racked up his 28th save for the American League West-leading Athletics, who won their second in three games against the Angels.
Los Angeles had led 1-0 since the second inning but Josh Reddick drew a leadoff walk in the seventh against Dane De La Rosa.
Jed Lowrie added an RBI double later in the inning.
Josh Hamilton cracked a solo homer for the Angels.
2014: The Year in Music [PHOTOS]