The loss marked Boston's fourth consecutive setback in a series opener and snapped a four-game winning streak against the Royals dating back to May 19, 2008. The setback also allowed New York to move into a first-place tie with Boston atop the American League East.
"We've turned it over to our bullpen a lot of times this year and been in pretty good shape," manager Terry Francona said. "We just couldn't hold them down in the sixth."
The Sox (51-34) raced out to a 3-0 lead in the first, an inning highlighted by David Ortiz's 300th career home run. Following an RBI single from Kevin Youkilis, the slugger smashed a line drive to left off Kansas City starter Luke Hochevar that barely cleared the red line along the top of the Green Monster.
Jason Bay plated Youkilis (2-for-5, two runs) with a single to center in the third, giving the Red Sox a four-run lead after three innings.
Starter Brad Penny, however, came undone in a three-run fourth for the Royals. After Miguel Olivo hit an RBI single to right, Jason Varitek's throw to second on a stolen base attempt by Olivo sailed into center field, allowing Mark Teahen to score from third.
Callaspo pulled Kansas City (37-48) within a run with an RBI double off Penny, who allowed three runs on six hits in five innings of work. The righty has surrendered three runs or fewer in nine of his past 10 outings, but he lamented his inability to pitch deeper into Thursday's game.
"My job as a starter is to go more than five innings," Penny said.
Dustin Pedroia powered a high fastball from Hochevar (5-3) into the Monster seats in the fifth, but the Royals answered one inning later with their four-run bulge.
Freel's bloop RBI single with two outs set the stage for DeJesus, who sent a Masterson offering into the Kansas City bullpen.
"It was a fastball that was supposed to be away, and it ends up right at his bat," said Masterson (3-3), who was charged with his first blown save of the season.
"You look back, and one pitch hit a guy's bat and that's the game," he added. "But that's part of baseball. They're professional hitters. The bullpen can't always get everyone out, but we try to do a good job at it."
Down to their last six outs, the Sox threatened in the eighth. Mark Kotsay's bases-loaded sacrifice fly trimmed Kansas City's lead to two runs, but with runners at the corners and two out, Royals closer Joakim Soria struck out Nick Green on a soft breaking ball to end the threat.
Despite the recent struggles of Boston's relief corps, Francona raised an eyebrow when asked if the unit is a cause for concern going forward.
"We love our bullpen," he said. "I think we have the best bullpen in the league. But when you look for four innings of relief, bad things can happen."
"We haven't caught a lot of breaks recently," Masterson said. "You're going to go through stretches like that. But if we keep firing, things will turn around, and we'll be OK."