Billy Butler singled in the only run of the contest in the first inning and the Royals then rode its outstanding pitching to snap a five-game losing streak.
Santana (6-6) retired the first 10 men he faced before giving up a single to Torii Hunter in the fourth. Detroit's only other hit was a two-out single by Andy Dirks in the fifth.
Kelvin Herrera relieved Santana after the Detroit starter walked a batter with one out in the eighth. Greg Holland worked a perfect ninth for his 23rd save.