CLEVELAND (AP) -- Grady Sizemore was confident as he strode to the plate in the bottom of the ninth inning.
"I knew I'd had success against him, but I was just thinking about how I was going to attack the at-bat," Sizemore said.
The big hit made Sizemore 5-for-9 with two homers and six RBI in his career against the Royals righty.
"I knew I hit it well," said Sizemore, hitting .354 over his last 25 games. "I was just hoping to get all three of them home."
The Indians won their third in a row and stopped Kansas City's three-game winning streak. Cleveland also beat the Royals for the eighth straight time at Jacobs Field.
"Everybody did what they needed to do to make that comeback possible," manager Eric Wedge said after the Indians improved to 2-53 this year when trailing after eight innings. The other late comeback win was 6-4 over Kansas City on May 16.
Burgos (2-5), who now leads the AL with 11 blown saves, relieved in the ninth with a 3-1 lead. But Ryan Garko and Ramon Vazquez each singled with one out and pinch-hitter Aaron Boone fouled off a pair of full-count pitches before drawing a walk.
"I only got one hit, but it was a big one and I'm happy to contribute," said Vazquez, who was recalled from Triple-A Buffalo before the game when Cleveland designated right-hander Guillermo Mota for assignment.
Sizemore hit an opposite-field liner that bounced off the wall, and when the carom got past left fielder David DeJesus, the winning run scored.
"It sure is the hard way to do it," Sizemore said of his first game-ending triple.
Of sliding into third base when he could have pulled up at second with a game-winning double, the All-Star outfielder grinned and said, "It was the adrenaline. I was in a hurry to celebrate with my team."
Royals manager Buddy Bell said he will remain patient with the 22-year-old Burgos.
"It's a learning process for him," said Bell. "He needs to understand what is a good pitch for him and what is not."
Fernando Cabrera (2-2) pitched a perfect ninth for the win.
The Indians' rally deprived Adam Bernero of his first win as a starter in more than three years. The Royals dropped to 15-41 on the road this season.
The Royals purchased Bernero's contract from Triple-A Omaha before the game. He made the call-up worthwhile, allowing one run and seven hits over 5 2/3 innings, striking out five without a walk.
"I was keeping the ball down, locating it well," said Bernero. "It felt good to be out there."
Bernero gave up eight runs in two innings in his only previous game in the majors this season, for Philadelphia in an interleague game against Toronto on June 20. He was later released by the Phillies, signed a minor-league contract with the Royals on July 12 and had his contract purchased from Triple-A Omaha on Friday.
The Royals scored twice in the fifth off Paul Byrd with a series of soft hits.
Angel Berroa beat out a slow roller for an infield single but was promptly picked off first by Byrd.
With two outs, speedy Joey Gathright singled to center and took second when Sizemore bobbled the ball for an error. DeJesus singled off Jhonny Peralta's glove in the hole at short and Mark Grudzielanek looped a single for one run. Mark Teahen hit a soft liner over Peralta's head for a 3-0 lead.
Emil Brown hit a sacrifice fly in the first inning to put Kansas City ahead 1-0.
Byrd allowed three runs and 10 hits over eight innings, walking two and striking out two against his former team. The right-hander went 17-11 for Kansas City.
Byrd got a pregame visit from his college coach at Louisiana State, Skip Bertram, who is now the school's athletic director. ... Indians catcher Victor Martinez singled in the fourth for his 500th career hit.