Choo was a major factor in the Indians' two-run rally in the eighth that tied the game, and he came through with the game-winning hit off Kyle Farnsworth (1-4).
Farnsworth surrendered a leadoff single to DeRosa, walked Victor Martinez and then gave up the base hit to Choo that allowed the Indians to win their second game in the three-game series.
Choo also drove in a run with a fielder's choice grounder in the eighth and scored the tying run on a double by Jhonny Peralta.
Matt Herges (2-0) got the win by working the top of the 10th.
Kansas City starter Zack Greinke failed in a bid to win his ninth game of the year. He allowed three runs on six hits with three walks and six strikeouts over 7 1/3 innings, but came away without a decision.
The Royals are 2-5 in Greinke's last seven outings after he had won his first six starts of the season.
Copyright 2009 by United Press International.