With the game tied at 2, Sanchez fired a 3-1 fastball at the letters to Detroit's Delmon Young in the sixth inning, which Young deposited into the left-field stands for the winning margin.
However, it was an encouraging start for Sanchez, who has struggled this season. He was economical in his first two innings, allowing just one hit over 25 pitches. But Sanchez made two critical mistakes.
The first came on a hanging slider to rookie Quintin Berry, who tripled in a pair of runs in the third for an early 2-0 lead. The second was the fastball to Young in the sixth that caught too much of the strike zone.
"I was around the plate and did some good things," said Sanchez, who allowed four runs on six hits with three walks and two strikeouts in 5 2/3 innings.
"But the results weren't good."
Yost said that Sanchez's effort was a step in the right direction and he was encouraged by the outing.
"His strike-to-ball ratio (60 strikes, 41 balls) was better and his command was better," Yost said. "He kept us in the game. It was something to build upon. If he keeps the ball down like he was [for most of the game] he's going to get a lot of outs."
While Sanchez was giving his teammates an opportunity to win, the Royals' offense was scuffling. Kansas City's hitters clearly weren't seeing the ball well early against Detroit rookie Drew Smyly (4-3) when the sunny and shady hitter's backdrop at Comerica Park favored the pitchers, according to Yost.
The southpaw, who fanned a career-high 10, struck out four of his first six batters swinging and dusted the side in the second -- freezing Jeff Francoeur with a fastball on the inside corner for the final out.
"My curveball was on so well," Smyly said. "It was kind of slurvy, but over the past couple weeks, me and [pitching coach Jeff Jones] have been working. ... I threw a lot of them in the dirt, and they were swinging at them over and over. That tells me they were thinking it was something else."
Smyly again struck out the side in the fourth inning, retiring the Nos. 2 through 4 hitters, and getting All-Star Billy Butler to chase a nasty curveball for strike three and the third out. It was that kind of night for a Kansas City offense that has averaged 68 runs in their past 12 games (5.66 runs per game).
"He's got a good fastball and curve, and he pounds the strike zone," said Royals first baseman Eric Hosmer.
Catcher Brayan Pena, whose RBI double sparked a two-run fifth that got the Royals even at 2, said the key to Smyly's success was keeping the ball down out of the zone.
"You can tell he's starting to feel more comfortable [pitching in the Majors]," Pena said. "He gave them what they needed."
The Royals finally got to Smyly in the fifth, as Mike Moustakas led off with a ground-rule double to center. With two outs, Pena and Jason Bourgeois delivered back-to-back hits to get the Royals on the board.
The Royals threatened again in the sixth.
Billy Butler delivered his second hit of the night and Yuniesky Betancourt followed with a double off the glove of Detroit left fielder Young against the fence. But Smyly induced Moustakas to bounce out to first on his 106th and final pitch.
Sanchez matched his second-longest outing of the season.
"It was a much better outing for him," Pena said. "He was attacking and throwing more strikes. And he was mixing his pitches well and hit his spots. "He was able to get [Prince] Fielder and [Miguel] Cabrera in the third inning with a runner at third [and one out]."
Jose Mijares worked 1 1/3 scoreless innings in relief, while Louis Coleman allowed one hit and one intentional walk, but struck out the side in the Detroit eighth.
The Tigers used four relievers to get the final nine outs, allowing just one baserunner during the final three innings. Closer Jose Valverde notched his 16th save of the season.
"We weren't able to get to Smyly when we had two runners on [in the sixth inning] and we faced some really good pitchers after that," Yost said.