Saunders (5-1) allowed five hits, all singles, walked one and struck out six for his second career complete game and his fourth straight win.
Greinke (6-1) went the distance for the fourth time this season and for the seventh time in his career, but a sacrifice fly by Chone Figgins in the third inning cost him his first loss of the season.
Greinke's season ERA rose to just 0.51. Greinke was trying to become the first Kansas City pitcher to win his first seven starts of the season.
Kendry Morales had two of Los Angeles' four hits, as the Angels won for the sixth time in their last seven games.
Copyright 2009 by United Press International.