On his fourth try, Scherzer (10-4) finally got his 10th win, allowing one run on six hits over 6 2/3 innings.
"I didn't walk anybody," Scherzer said. "I didn't put myself in dangerous positions. I was able to keep the ball on the ground and was able to have a good outing."
Danny Duffy (1-4) suffered the loss, allowing two runs on four hits over six innings. He struck out six and walked one.
"It's what's best for the team," said Duffy, who was set to minor leagues after the game. "We've got another arm in the bullpen. I don't fret over that. I'll go down to Omaha and do what I've got to do. Get a start and work on getting back here on the (July) 18th and do it against the White Sox on 19th."
Raburn blasted a two-run homer over the fence in left to break open the scoring during the second inning.
Kansas City got a run back in the fifth, which was started by Eric Hosmer's double. He moved to third on a Jeff Francoeur fly out in foul territory and scored on Moustakas' groundout to second.
Kelly added an insurance run in the ninth with a leadoff shot over the fence in right.
Jose Valverde came into the ninth and got two quick outs before walking Hosmer. Later on, Francoeur singled and stole second to put runners on third and second. Moustakas, who represented the winning run flied out, though, to end the game and give Valverde his 22nd save of the season.
Detroit's Austin Jackson left the game with left wrist soreness...Alex Gordon has an eight-game home hitting streak...Detroit is 4-2 against the Royals this season...KC was just 1-for-8 with runners in scoring position and left six men on base... The Royals out-hit the Tigers 8-6.