Buchholz, who missed much of last season with a stress fracture in his back, struck out two and walked two.
Jason Marquis struggled in his debut for Minnesota, allowing four runs in 1 2-3 innings.
Boston scored four times in the second and led 5-0 after three. Backup catcher Daniel Butler added a three-run homer in the seventh inning.
Joe Mauer went 2 for 3 with an RBI for Minnesota.