Young ripped a 1-0 pitch from Kyle Farnsworth (0-3) into the seats in left-center for his first career game-winning homer. Young leaped into the air as he approached home plate, diving into a group of teammates there to greet him.
Frank Francisco (1-0) pitched the ninth for the win.
The Rangers trailed 5-3 when Andruw Jones doubled off reliever Ron Mahay in the eighth. Jones went to third when Royals first baseman Mike Jacobs booted Hank Blalock's grounder, and he scored on Nelson Cruz's ground-out off Jamey Wright to make it 5-4.
Blalock went to second and Chris Davis followed with a pinch single, and Blalock scored from second when the sharp grounder glanced off the glove of second baseman Alberto Callaspo.