"It's not easy right now. My stomach, I've got a knot," Detroit manager Alan Trammell said. "I don't like it at all. I am in charge so it is my responsibility. It bothers me. I'd love it to stop as quick as it possibly could."
Detroit's losing streak is its longest since dropping 10 straight in September 2003 during its AL-record 119-loss season.
Kansas City had a club-record 19-game skid earlier this season.
Zack Greinke (4-16) won for the first time since July 19. He gave up one run on five hits in 5 2/3 innings. The AL leader in losses had been 0-5 in eight outings since his last win.
"This year has been like that," Greinke said. "I don't even know how long it's been. The whole year seems like a bunch of losses."
"I know it looked bad," Greinke said. "He had hammered the ball on the first pitch last time, so I tried to go in."
"Because of the history and Ambres got hit earlier," Kansas City manager Buddy Bell said, "I guess Mike (home plate umpire Mike Everitt) felt like Zack sent a message."
Sean Douglass (5-4) lasted two innings and allowed four runs and four hits, walking one and striking out four.
"You look at some of the plays they made tonight," he said. "They made unbelievable double plays. We hit line drives right at them. That's just the way things have been going."
Kansas City took a 1-0 lead in the first on Stairs' two-out RBI double. The Royals added three in the second on Huber's run-scoring double and Guiel's two-out, two-run homer.
"The hitting became contagious and everything just clicked," Guiel said.
Kansas City made it 7-0 with three more in the fourth on Terrence Long's RBI triple, and run-scoring singles by Stairs and Angel Berroa.
Detroit got a run in the fourth on Magglio Ordonez's fielder's choice, but the Royals added three more in the fifth on Brown's three-run double.
Ambres doubled in a run in the seventh. Buck hit a solo homer in the eighth, his 10th of the season.
- Kansas City activated INF Donnie Murphy from the 15-day disabled list on Friday. He had been placed on the DL because of a right finger fracture on Aug. 25.
- Detroit has scored six runs in its last six games.
- The Royals sent RHP D.J. Carrasco back to Kansas City because of tightness in his right shoulder.