The bullpen got nicked for four runs, only two earned, over the final five-plus innings, unable to preserve an 8-6 lead.
"The 'pen has just been dynamic lately," manager Ned Yost said. "It's just one of those nights, they weren't exceptionally sharp."
Leading 8-6 in the seventh, the Royals went to recently acquired left-hander Ryan Buchter, who promptly walked the first two hitters he faced. A passed ball moved a runner into scoring position, and a sacrifice fly by Jackie Bradley Jr. brought the Red Sox within 8-7.
"Buchter was just missing, by an inch or two," Yost said.
Joakim Soria took over in the eighth and he gave up two sharp singles and a sacrifice fly, and the lead was gone.
When the Royals didn't score in the ninth or 10th, it was up to left-hander Mike Minor to keep it tied. Minor wiggled out of a two-on, one-out jam in the ninth, but Sandy Leon's leadoff double in the 10th put Minor in a precarious spot.
After a strikeout, the Royals intentionally walked Mookie Betts. But then, Minor's second wild pitch of the night moved the runners up, forcing the infield in.
"I was ahead in the count," Minor said. "You're trying to get them to chase."
Then, Eduardo Nunez hit a hard grounder up the middle: Shortstop Alcides Escobar made a diving stop on his knees and threw out Nunez. But Leon broke for the plate and beat first baseman Eric Hosmer's throw home with a great slide.
"I didn't even know where Esky was playing behind me," Minor said. "Obviously, we were playing in and he made a great play. I was really surprised [Leon] didn't go right away, and when he didn't go, I thought that this was our second chance here. I was sure he wouldn't break the second time."