The Red Sox jumped out to an early 8-0 lead and cruised past the Royals 10-5 in Kansas City.
Mookie Betts led off the game with a home run and J.D. Martinez and Xander Bogaerts launched two-run bombs in the second.
Chris Sale struck out 12 across six frames of one-run ball to earn the win. Boston has won four-straight and improved to 60-29.
Jason Hammel was battered for eight runs over two innings as he fell to 2-11 for the Royals.
Kansas City is on a seven-game slide.