Chen treated the 21,121 fans to 7 2/3 shutout innings. Mike Moustakas delivered a two-out, two-run single in the first inning, and Billy Butler and Justin Maxwell each belted a solo homer in the eighth.
The Red Sox top the AL with a 70-47 record, a stout 23 games over .500. They are 12-8 since the break.
"That's a great team over there, and we're a good team over here, too, and we were able to beat a great team today," Moustakas said.
The Royals were going against Jon Lester, a lefty who usually does things right against them, and they rustled up three runs in the first inning. Of course, a misplayed pop fly proved to be a valuable help.
Lester opened the series with a 6-2 record in nine career starts against Kansas City that included a 2008 no-hitter and a 1.64 ERA, the lowest by any pitcher who had pitched at least 50 innings against the Royals.
"If you're going to get a guy like Jon Lester, you better do it in the first inning," Royals manager Ned Yost said. "To get three on the board early was big, it allowed Bruce that little breathing room we always talk about. And then Jon found his gear and made it through the seventh inning. He pitched a great game, too."
Lorenzo Cain opened up against Lester with a double and Butler walked with one out. With runners at the corners, Alex Gordon hit a lazy fly ball to left field toward Jonny Gomes, who had his mind on Cain tagging up at third base.
Gomes intended to lay back and then run hard to make the catch, giving him plenty of momentum for a throw to the plate.
"I got behind it, but my plant leg slipped and took a chunk out of the grass," Gomes said. "I just couldn't make up the ground."
Gomes had to make a futile last-minute lunge. He trapped the ball and tried to sell it as a catch, but third-base umpire Greg Gibson got the call right and Cain scored. Gomes was charged with an error and Gordon was credited with an RBI on the sacrifice fly and stood on first base.
After an out, Maxwell walked to load the bases and Moustakas lined a two-run single to right field. Lester struck out Brett Hayes but the Royals had a 3-0 lead.
"That's what we've been doing," Moustakas said. "We've been taking advantage of the other team's mistakes and that's a sign of a good team."
After that, Lester got into a groove and lasted through the seventh inning without further damage so the big first inning was crucial.
"In the past, we haven't fared too well off of him, but like we've been saying in here, we're a different team now. The confidence has been there," Butler said. "It means everything in the world to come out of the gates."
After 121 pitches, Lester yielded to Rubby De La Rosa in the eighth. He was greeted by Butler's smash over the center-field wall, 413 feet away. After two outs, Maxwell connected with a homer to right field.
"Maxwell just crushed it, and so did Billy," Yost said. "Anytime you can take a ball out to center field here or the opposite way here, you really have to smoke a baseball and both of those kids did that."
Chen, who has a 1.14 ERA in five starts since joining the rotation, was on a steady course. Jacoby Ellsbury started the game with a single to center but was promptly caught off first base by Chen and thrown out at second. Through the seventh inning, Chen had given up just three more singles and one walk with no runner going past first base.
In the top of the eighth when the Royals' lead was still 3-0, a leadoff single by Daniel Nava and a two-out hit by Ellsbury prompted a pitching change.
"I wasn't going to let the tying run come to the plate [against Chen]," Yost said. "Bruce wasn't going to face it -- one. And two, I made my mind up early in the game that I wasn't going to let Bruce face that lineup a fourth time around and Ellsbury was the only one that did that."
Right-hander Luke Hochevar came in to face switch-hitter Shane Victorino and got him to pop out.
After the two homers, there was no immediate need for closer Greg Holland, so Hochevar went out to pitch the ninth. Gomes hit a one-out double to center and scored on Stephen Drew's single. By then, Holland was warming up, but Hochevar got Mike Napoli to ground into a game-ending double play for his second save.
With Detroit winning its 12th straight game, the Royals remained 8 1/2 games out of first place in the AL Central and 4 1/2 games behind in the AL Wild Card race.
But they're undaunted.
"Everyone seems to be inspired and I think it's going to be some fun times," Chen said. "But we have to keep it going and keep the momentum."