Chris Sale had time to catch his breath. Now, maybe, he’s locked in.Sale pitched eight solid innings, Paul Konerko and Gordon Beckham hit home runs late, and the White Sox beat the Kansas City Royals 4-2 on Monday night.The margin for error is slim, with a 1½-game lead over Detroit for the AL Central lead. The Tigers are playing well, but so are the White Sox. And they pulled this one out thanks to a strong start by their pitcher and some big hits toward the end.Konerko tied it leading off the seventh and Beckham gave the White Sox a 3-2 lead with a solo shot in the eighth off Luis Mendoza. Kevin Youkilis added an RBI double in the inning, and the White Sox won for the 10th time in 13 games.A.J. Pierzynski added two hits, and although he didn’t go deep after tying a club record with home runs in five consecutive games, he did drive in the first run with a double in the second. Sale (13-3), meanwhile, looked sharp on nine days’ rest, allowing two runs and eight hits while striking out seven without a walk. He gave up solo homers to Jeff Francoeur and Billy Butler, but otherwise kept the Royals off-balance, with his fastball consistently in the mid-90s mph.Sale was passed over during the last time through the rotation. The White Sox wanted to give him more rest in his first year as a starter.Addison Reed worked the ninth for his 20th save in 23 chances, retiring Eric Hosmer on a double-play grounder with runners on first and second to end the game. Mendoza (5-8) gave up seven hits and four runs in 7 1/3 innings. Butler made it 2-1 in the seventh with his 21st home run. Konerko tied it in the bottom half with a line drive to left that just cleared the wall and landed in the bullpen.The Royals had runners on first and third in the eighth, but Sale got out of it. Shortstop Alexei Ramirez made a diving stop on Alex Gordon’s soft liner. Sale tagged out Tony Abreu trying to score on Alcides Escobar’s safety squeeze and struck out Lorenzo Cain on three pitches, pumping his left fist on the way to the dugout.

NOTES—White Sox LHP John Danks had surgery on his left shoulder on Monday, and the team expects him to be ready for the start of spring training. Danks’ arm is expected to be in a sling for a month. Doctors at Chicago’s Rush University Medical Center repaired a capsule tear and removed debris in the rotator cuff and biceps….Robin Ventura said LHP Francisco Liriano sustained no real lingering effects after being struck in the right quadriceps by Maicer Izturis’ one-hopper in the fifth inning against the Los Angeles Angels on Sunday. Liriano left after five innings….Royals manager Ned Yost would not comment on a pregame meeting in the clubhouse. “It’s a meeting between us,” he said. “If I wanted you guys to be part of the meeting, I would have invited you.”….The Royals held 3B Mike Moustakas out of the lineup for the second successive game because of a lingering bone bruise on his right knee. He first hurt his knee on a fielding play in the first inning July 28 at Seattle….Gordon was back in the Kansas City lineup, leading off and playing left field, after sitting out his first game of the season on Sunday….Jake Peavy will start Tuesday, with Bruce Chen pitching for the Royals.