Young, the first overall pick in the 2003 draft, hit his 20th homer with one out in the seventh on a full-count changeup from Gil Meche (0-5). The ball clipped the left-field pole.
Young's single in the ninth scored Orlando Hudson, who had doubled, with the final run.
Capps had to work around a leadoff pinch-hit single by Gregor Blanco and a walk to Jarrod Dyson. He struck out Mike Aviles and ended the game with Billy Butler grounding into his major league-leading 31st double play.
The Royals took a 2-0 lead in the second. Rookie Kila Ka'aihue led off with his eighth home run. He hit two home runs Tuesday. Lucas May's single scored Alex Gordon, who had walked and advanced to third on a double by Yuniesky Betancourt.
The Twins tied it in the sixth when Royals right-hander Luke Hochevar gave up singles to Michael Cuddyer and Danny Valencia, who had three hits, and walked Jason Repko to load the bases with one out. Drew Butera lined a single to left to score Cuddyer. Alexi Casilla's fielder's choice groundout scored Valencia with the second run.
Twins starter Scott Baker, who missed three September starts after receiving a cortisone shot in his right elbow, left after five innings, allowing two runs, six hits and four walks, striking out nine.
Matt Guerrier (5-7), the second of four Minnesota pitchers, picked up the victory, striking out four of the five batters he faced. The Royals struck out a season-high 15 times.
The Royals stranded eight runners from the second through fifth innings, going 1 for 11 with runners in scoring position in that span.
Hochevar, making his final start of the season, gave up two runs and seven hits in six innings.
Notes: Twins 1B Justin Morneau, who has not played since July 7 because of a concussion, is scheduled for a full workout before the game Thursday at Target Field. ... Royals OF Mitch Maier missed his fourth straight game with a sore left knee. ... The Royals have won 65 games, matching their win total for 2009, but have lost 93 games, the eighth time in the past 10 seasons they have lost 90 or more.