The rookie Boston third baseman launched a three-run shot in the first inning and added a two-run blast in the ninth and has collected an extra base hit in all four major-league games in which he has played.
Dustin Pedroia hit a two-run homer and scored three runs while David Ortiz went 3-for-4 with and RBI and scored three times for Boston, which pounded out 16 hits.
Felix Doubront (2-1) earned the win despite allowing four runs on seven hits through 6 1/3 innings.
Royals starter Jonathan Sanchez (1-2) was lit up for six runs on six hits before exiting after three innings.
Alex Gordon had two hits and an RBI for Kansas City.