The Royals, who have not made the playoffs since 1985, are 2 games back in the wild-card standings, while the Indians are a half-game behind.
"I felt really good about Bruce being on the hill for us," Yost said. "I just felt his veteran experience was going to be crucial in a big game like this. My mindset was to get him through the lineup twice and if we had any lead at all, to do some maneuvering.
"A game of this magnitude you don't play around. We've got 10 games left. You don't play [around] with 10 games left especially when they are this big. You get it out of the way and then you worry about tomorrow tomorrow."
Yost did some bullpen maneuvering to keep the lead.
"Every single game is a must win," Chen said. "We're behind. We're trying to catch up. The bullpen did an outstanding job. We have the best bullpen in the American League."
"He does what he does," Indians manager Terry Francona said of Chen. "He's up, down, in, out. Nothing the same speed. He takes the sting out of your bat. He really knows how to pitch."
Francisley Bueno replaced Chen and recorded two outs with three pitches.
After Jason Kipnis advanced the runners with a sacrifice bunt, Bueno kept the runners put when Carlos Santana grounded out to third baseman Mike Moustakas. Louis Coleman came in and retired Ryan Raburn on a fly to right to strand the runners.
The Royals broke the game open with three runs off four Indians pitchers in the eighth. Alcides Escobar had a two-run single on a full-count off Carlos Carrasco, while Jarrod Dyson walked with the bases loaded.
"The last at-bat, that's one of my best at-bats of the year," Escobar said. "I was just trying to put ball in play, ground ball, fly ball, anywhere. I was really concentrating. I was trying to put the ball in play and got the base hit."
Rookie Danny Salazar (1-3), who had allowed just one run in 13 2/3 innings in his first three September starts, took the loss, giving up four runs and six hits in six innings.
The Royals used a double steal in the fifth for their fourth run. Escobar avoided the tag of catcher Gomes to steal home, while Alex Gordon, who was initially caught in a rundown, stole second. Escobar became the first Royal to steal home since Jeff Francoeur on Aug. 11, 2012, at Baltimore.
"I was kind of looking to take him back to third base and peaked (at the other runner) and when I did that he kind of dropped and went under my tag," Gomes said.
The Royals recalled LHP Chris Dwyer, who allowed one single and struck out eight in seven scoreless innings for Omaha in the Triple-A 2-1 championship victory over Durham on Tuesday, and IF Irving Falu, who hit .256 in 135 games with the Storm Chasers. Falu was with Kansas City for one day, Aug. 11, but was optioned back to Omaha the next day without playing. ... Indians RHP Justin Masterson, a 14-game winner who is out with an oblique strain, threw 120 feet in long toss and made 20 to 25 pitches off flat ground. ... The Indians won the season series from the Royals for the ninth time in 10 years.