"I just told him, 'You know Erv, you had a great year. Real proud of you.' That was it," Yost said.
Miller pushed a bunt up the first base line and reliever Will Smith's throw to first baseman Eric Hosmer was wide, allowing Ackley to score.
The Royals' best offensive chance came in the fifth, when Mike Moustakas doubled with one out and took off running when Jarrod Dyson hit a line drive which looked as if it might reach the outfield.
Instead, Miller at shortstop timed his jump and snared the ball, then jogged to second to double off Moustakas and end the inning.
The Royals, who were six games below .500 at the All-Star break, head to Chicago to finish up the season with a four-game series against the White Sox.
Even without a shot at the playoffs, Kansas City (83-75) is assured of its first winning season in a decade, and one more win will give them their best record since they finished 84-78 in 1993.
"We've had a real good second half," Billy Butler said. "We have one more series and we get to build on this for next year. We had a good run, and the guys in here played hard."
Yost said he'll have a chance to give some young players an opportunity over the final four games, but doesn't expect any letdown despite no longer having a shot at the postseason.
"I think we've made a lot of progress as an organization," Yost said. "It was a giant step forward for us, and it was a step we definitely needed to take this year."
NOTES: Seattle manager Eric Wedge said before the game he feels like he's "hanging out there" with little clarity regarding his future with the organization. Wedge's contract — originally a three-year deal — expires after the season and Wedge indicated he's been given no word about whether he'll return for a fourth year. ... Seattle has hit 183 home runs this year, tied with Toronto for second-fewest in the major leagues. ... The last time Kansas City was shut out in back-to-back games was May 22-23, 2009, at St. Louis.