Sale allowed more than two runs in a game for the first time since May 12. Snapping his five-game winning streak, he gave up a career-high five runs in 5 2/3 innings.
"Have to be better. It was everything this team did not need from me tonight," said Sale, whose ERA rose from 2.05 to 2.46. "I was all over the place early, got banged up late. I've just got to be better."
Sale allowed seven hits, issued a career-high four walks and struck out six.
"Walking the first guy of the game, walking a few more guys after that, throwing the ball all over the place, they took advantage of that," Sale said. "They got the pitch count up there."
Sale didn't show his usual command, White Sox manager Robin Ventura said.
"Walking the first guy or a guy leading off an inning, he doesn't do that," Ventura said. "He's going to let them put it in play and see what happens. Today was just one of those days."
"He's good. His stuff is good," Dodgers manager Don Mattingly said about Sale. "It looked like he was a little bit erratic with his command tonight more than we've seen usually, but he was the same guy we've seen in Spring Training. He's one of those guys who's long and lanky and he gives you that little whip in the arm. He changes speeds well. He's tough."
The White Sox gave Sale a 5-1 cushion heading into the bottom of the sixth. The National League West-leading Dodgers (41-24) rallied for five runs in the inning via five hits and a walk. After Jesse Crain replaced Sale with two runners on base, Elian Herrera hit a two-run double to tie the game, 5-5, before Juan Rivera's single drove in the go-ahead run.
Meanwhile, Kershaw, the 2011 NL Cy Young winner, was also struggling. He tied a season high by allowing five runs (four earned) in six innings. He struck out seven, walked two and gave up eight hits, including two home runs.
"You get five off him, you feel pretty good about it," Ventura said.
Adam Dunn hit his Major League-leading 23rd home run, a two-run shot off Kershaw in the first inning. Dunn has homered in five of his last six games. He entered the game batting .636 (7-for-11) with three home runs in his career against Kershaw.
Dunn now has 52 RBIs after driving in 42 runs last season.
"[I'm] not surprised, but you're happy for him after everything he went through last year," Ventura said. "It's just nice for him to do it. But it's not surprising."
Alex Rios hit a solo home run against Kershaw in the fifth inning, the first of his two home runs of the night.
After the Dodgers rallied to take a 6-5 lead, Rios tied the game with a solo shot off Ronald Belisario in the eighth for his eighth home run. It was Rios' fourth career multi-homer game and his first since 2008.
"He's been swinging it really good for us, showing some power as of late," Ventura said.