The Royals have lost seven straight, including their first six games at Kauffman Stadium, the most consecutive home losses in franchise history to start a season. The Royals lost their first five at home in 1993.
Gerald Laird led off the inning with a single off Herrera, advanced to third on Cabrera's two-out single and scored on Mijares' wild pitch. Fielder singled home Cabrera with the go-ahead run.
"Miguel was the batting leader," Fielder said. "We're trying to be good hitters in that situation. That's what the situation was. That's just being a baseball player."
Cabrera, who snapped an 0-for-22 slide Tuesday, and Fielder combined to go 4 for 9. Fielder also stole his first base of the season.
Royals manager Ned Yost was second-guessing himself for not intentionally walking Fielder after Mijares' wild pitch moved Cabrera to second with two out.
"The first time it was just a good case of hitting," Yost said of Cabrera's single beating a shift. "The second time was pure stupidity on my part, plain and simple that's what it was. After the wild pitch, we had a runner on second. I started to overthink the situation." Scherzer (1-1), who had given up 10 runs and 13 hits and three walks in 8 2-3 innings in his first two starts, held the Royals to three runs and seven hits and one walk in six innings. Scherzer lowered his ERA from 10.38 to 7.98.
"It's always good to get a win here," Scherzer said. "I was able to work around some trouble. I executed some pitches and they were hitting them. They have a good hitting lineup. The offense gave us a lead and the bullpen got some key double plays. That's what those guys do. We've got four or five guys who can come in and give you a quality appearance and get some guys out when you need it. That's big."
Alcides Escobar's home run in the third gave the Royals a 2-1 advantage, their first lead in 27 innings and the second one of the homestand.
Royals left-hander Jonathan Sanchez, who was starting on three days' rest for only the fourth time in his career, pitched out of a bases-loaded, no-out jam in the fourth.
Sanchez left after five innings and 97 pitches, giving up two runs and four hits, while striking out three and walking three. Jhonny Peralta singled in the second for the first Detroit run, and Fielder's two-out fifth-inning double to right-center scored Cabrera with the other run off Sanchez.
Jose Valverde worked the ninth for his third save in four chances. Valverde got Escobar to ground into a game-ending double play.
The dugouts and bullpens emptied briefly in the bottom of the seventh when Quintero was hit by Scherzer's pitch to lead off the inning. Quintero had words with Tigers catcher Laird before going to first base, which led to the players streaming onto the field. Words were exchanged, but no punches.
"He slammed the bat down and I said something to him about it," Laird said. "I don't like to have the bat thrown down at my feet like that. We talked about it and it's fine."
NOTES: 2B Yuniesky Betancourt batted second, the sixth Royals player to hit in the No. 2 slot in the first 12 games. ... Tigers RHP Octavio Dotel is one appearance shy of appearing in his 700th game. He would become the 93rd pitcher in big league history to appear in at least 700 games. ... The Tigers are 38-19 at Kauffman Stadium since Jim Leyland took over as manager in 2006. ... The Royals have two blown saves in four opportunities. They are without closer RHP Joakim Soria, who is out for the season because of elbow surgery.