Matsuzaka (1-3) was activated off the disabled list to make the start against the Royals and answered with a five-hit effort over seven innings. He walked two and struck out six.
It was his first win in 15 months. Matsuzaka had been on the disabled list recently because of a neck issue but was also coming off so-called Tommy John surgery in June 2011.
The Royals' lone run was scored in the first inning without benefit of a hit. Jarrod Dyson walked to open the game. He stole second and took third on an error by Dustin Pedroia. Alex Gordon then delivered a sacrifice fly. Only one other Kansas City runner got as far as third on the day.
Boston's Jacoby Ellsbury answered with a home run down the right-field line and tied the score in the bottom of the first. It was his second home run of the season.
The Red Sox added two-run rallies in each the third and sixth innings to beat Luke Hochevar (7-12), who gave up eight hits and four earned runs over eight innings. He walked one and struck out six.
Celebrity Families of 2014 [PHOTOS]