Josh Anderson led off the 10th with a single and David DeJesus got to first on an error by Raburn. A groundout by Willie Bloomquist advanced the runners and the Royals then scored the game-winner on a throwing error by Raburn.
Mike Jacobs and Bloomquist each contributed an RBI for Kansas City.
Magglio Ordonez hit a solo homer for the Tigers.
Joakim Sona (3-0) got the win and Fernando Rodney (2-3) was the loser.