Merrifield battled Red Sox reliever Blaine Boyer through a seven-pitch at-bat before singling through a drawn-in infield. Two batters later, Lorenzo Cain singled in Merrifield, who had gone to second on a groundout.
The Red Sox fell a half-game behind the idle Yankees atop American League East. The Royals have won eight of nine.
Royals right-hander Jason Hammel tossed his fourth straight quality start, going seven innings while giving up seven hits and two runs while walking none and striking out four.
Red Sox rookie right-hander Hector Velazquez made his second career start and held the Royals to two runs over 5 1/3 innings.