White Sox starter Jake Peavy figured he threw a good pitch to Alcides Escobar in the third inning, when the Royals shortstop took him deep. It was just the wrong pitch at the time.

The seventh inning was a different matter entirely.

"The pitch to him later in the game, there's no excuse for that," Peavy said of Escobar's solo homer, which broke a 3-all tie Saturday night. "It was a sinker that ran back over the plate, not much on it — not much action on it."

In other words, it was the right pitch, just executed poorly.

Jeff Francoeur and Lorenzo Cain tacked on insurance runs in the eighth inning, and the Royals bullpen held on for a 6-3 victory that evened the three-game series.

"Escobar got him a couple of times," White Sox manager Robin Ventura said of Peavy, one of his All-Star pitchers. "Other than that, he was in it. That's the way it goes."

Escobar had just two homers all season and 11 in his career before he connected for a two-run shot in the third. White Sox slugger Adam Dunn homered and Dayan Viciedo hit an RBI triple in the sixth to tie it at 3, before Escobar went deep again for the first multihomer game of his career.

"I'm working out in the gym and I'm feeling very comfortable," Escobar said. "I'm the same guy, though, just trying to hit the ball in the middle."

Greg Holland (3-2) won in relief for Kansas City, while Jonathan Broxton rebounded from a blown save the previous night to retire the White Sox in order for his 22nd save of the season.

Broxton pumped his fist after finishing the game — and all the Royals fans that were in the ballpark Friday night probably did the same. Broxton gave up a run in the ninth in the series opener to turn a potential victory into a 14-inning, 5½-hour affair.

The White Sox eventually won the game on Kevin Youkilis' sacrifice fly.

The Royals and White Sox are no strangers to close games at Kauffman Stadium, though. They had gone to extra innings in seven of their previous 21 meetings.

This one appeared to be headed that direction most of the night.

The White Sox struck first when Gordon Beckham, who had the winning run Friday night, walked with one out in the third, and Alejandro De Aza's double to left field gave Chicago a 1-0 lead.

Kansas City answered in the bottom half of the inning when Jarrod Dyson singled to right, stole second and scored on Alex Gordon's single. Escobar followed with his third home run of the year, this one landing in the bullpen in left field and giving Kansas City a 3-1 lead.

"The pitch in the third to Escobar wasn't a bad pitch, but just the wrong pitch," Peavy said. "It was a ball that he got enough of to hit out of the ball park. Obviously, a big blow there."

The White Sox clawed back, though, just as they repeatedly did the previous night.

Dunn's homer leading off the sixth traveled an estimated 451 feet, clearing two different walls in center field — "I figured he hit it over the scoreboard," Royals starter Luke Hochevar said. Viciedo added a tying RBI triple off reliever Aaron Crow later in the inning.

The White Sox couldn't get him home, though, and the missed opportunity proved costly.

The White Sox just couldn't get enough offense to counter the Royals' late surge.

Peavy wound up pitching into the eighth inning for Chicago, throwing 120 pitches along the way. He still ended up losing for the fifth time in six starts. Much of the onus for that falls on his offense, which has managed a total of nine runs of support over that span.

"We beat a real good pitcher tonight," Royals manager Ned Yost said.

NOTES: Cain came in as a pinch hitter after starting Friday night. He missed nearly half the season with a multitude of injuries. ... White Sox manager Robin Ventura said Dylan Axelrod and Phil Humber will start against Boston, though he hasn't decided on the order for Tuesday and Wednesday. ... LHP Chris Sale will start the series finale Sunday for the White Sox. RHP Luis Mendoza will take the mound for Kansas City.