Dazzled by Daisuke
Matsuzaka held the Royals to only six hits and forced 10 strikeouts in seven innings.
In the top of the first, Boston's Manny Ramirez doubled to bring in Kevin Youkilis. In the fifth inning, Julio Lugo stole third base and scored after John Buck committed a throwing error, giving the Red Sox a 2-0 lead.
Kansas City's David DeJesus homered in the bottom of the sixth inning to give the Royals their only run for the day.
In the eighth, Boston's David Ortiz and J.D. Drew scored.
The Royals will host the Detroit Tigers at 7:10 Friday evening.