Dalbec, Boston's No. 9 hitter, singled in the second, put Boston ahead 2-1 in the fifth with his team-high third triple, was hit by a Jackson Kowar pitch in the seventh and hit a two-run homer in the ninth off Kowar.
Dalbec is 12 for 45 with four homers and 10 RBI in his last 12 games, raising his average to .214 and OPS to .699. He has nine homers and 32 RBI.
“We did a lot of good things today," Red Sox manager Alex Cora said. "We didn’t rely on the big guys today, so it was a good all-around win.”
Martín Pérez (5-4) allowed one run and three hits in five innings.
“Today I was attacking hitters well," Pérez said.
Brad Keller (6-7) lost his third straight start, giving up five runs, five hits and three walks in five innings.
Kansas City went 0 for 11 with runners in scoring position and stranded eight runners.
“We had some good chances with the offense, but we just couldn’t get it done," Royals manager Mike Matheny said.
Kowar allowed two runs, three hits and two wild pitches in three innings, but the 24-year-old rookie right-hander cut his ERA from 36.00 to 18.00 in three big-league appearances.
Kansas City's Whit Merrifield stole three bases, raising his major league-leading total to 20. But after swiping third base in the third inning with the score 1-1, he got caught off third on Salvador Pérez's comebacker and easily was tagged out in a rundown for the second out.
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