Eric Hosmer opened the Royals' 11th with a single off right-hander Esmil Rogers. Hosmer was sacrificed to second by Chris Getz and took third on a wild pitch. Jarrod Dyson popped out to center and Alex Gordon was intentionally walked. With that, the Indians replaced Rogers with closer Chris Perez.
No matter, on a 1-2 pitch Escobar bounced a single through the shortstop hole and he rounded first base -- throwing his helmet into the air as Hosmer scored to account for the Royals' fourth walk-off victory of the year.
"Knowing the top of the order's coming up and I've got some guys behind me, I was just trying to get on right there and have those guys move me over," Hosmer said. "Because the way Gordo and Esky have been swinging the bats, you just want to get on and get in scoring position for those guys."
It marked the Royals' first series sweep since they won three from Tampa Bay on June 25-27, also at home.
Corey Kluber, a 26-year-old right-hander, was summoned by the Indians from Triple-A Columbus to make his first Major League start and he was pummeled for six runs in the first inning. But after that he pitched into the fifth inning without allowing another run.
"I think there might have been some nerves in there in his first Major League start, and things kind of avalanched on him a little bit," Royals manager Ned Yost said. "He sat himself down, did a great job of composing himself and getting himself back in his game, and really shut the door on us from that point on."
Gordon hit Kluber's first pitch of the game over the right-field wall for his sixth home run. And it didn't get any better very quickly. Before the inning ended, the Royals had six runs on six hits -- including a three-run homer by Hosmer -- and a walk. Kluber faced 10 batters and threw 43 pitches.
Escobar singled, swiped second for his 19th steal and scored on Lorenzo Cain's single. Kluber got two outs, but walked Brayan Pena, and Hosmer launched a 1-0 pitch over the center-field wall, a 423-foot wallop for his 10th homer. It was a long wait between homers for both Gordon (188 at-bats) and Hosmer (116).
"Usually I like taking the first pitch, but every once in a while I change it up," Gordon said. "I told myself that if I got a fastball right down the middle, which I did, I was going to go after it. Anything else, I was going to shut down, but I got my pitch and was able to put a good swing on it."
The sixth run came as Getz tripled to right and scored on Dyson's single. And the Royals did not score again until the 11th.
Royals starter Bruce Chen gave up four runs and was chased in the third inning -- his seventh straight start without a victory.
"He's not throwing the ball good. He's not using his good fastball, he might've thrown three pitches over 85 miles an hour and it's in there. And he threw one 88; everything's soft and he's just not throwing the ball real well right now," Yost said.
"He needs to pick his game up. To put a 6-spot on the board is a pretty big cushion and to not be able to get out of the third inning, we need to do better than that."
Chen was relieved in the third by Everett Teaford and, by the fifth, the Royals' 6-0 lead had morphed into a 6-6 tie. Brent Lillibridge singled and stole second before Carlos Santana lined a two-run homer, belting a 0-2 pitch from Teaford just over the left-field wall.
"I was trying to be a little quicker so Lillibridge couldn't take third and the ball just backed up on me, and it's just terrible execution on my part," Teaford said.
Teaford was struck in the rear by Shin-Soo Choo's shot, but the pitcher recovered the ball and threw him out to end the sixth inning. Teaford was OK afterward but was replaced for the seventh by Kelvin Herrera, who struck out the side. That was just the prelude to a fine collective effort by the bullpen.
Herrera pitched two scoreless innings followed by a perfect inning each by Tim Collins, Greg Holland and Aaron Crow, who earned the victory.
"Our bullpen did a tremendous job of coming in and holding down the fort," Yost said. "Teaford made two mistakes and they were on 0-2 pitches and ended up costing him a win -- pitches that he just didn't finish -- but other than that he was really good. He stopped the bleeding and the rest of the bullpen guys were spectacular."
It was a case of good news followed by bad news for the sagging Indians, who lost their sixth straight game.
"I'm very happy that we were able to come back from a six-run deficit. We made it a heckuva ballgame," Indians manager Manny Acta said. "But their bullpen kept us down and they beat our best guy at the end to sweep us."