The left-hander gave up four hits in two innings and was charged with an error, allowing Chicago to grab a 2-0 lead. The White Sox went on to win 9-0.
"I feel good," said Kershaw, who was selected to make his third straight Opening Day start on April 1 against World Series champion San Francisco at Dodgers Stadium. "I feel strong. That's the important thing right now.
In the first, Chicago's Alejandro De Aza singled and took third off an errant throw from Kershaw in a pickoff attempt at second. De Aza scored off an Alex Rios' single. In the second, Kershaw gave up two hits and a run. Chicago's Alexei Ramirez singled and scored off a Gordon Beckham double.
"For the first day, things went all right. Obviously, you don't want to give up runs. But better now than April."
Unlike the Dodgers' ace, White Sox pitcher Dylan Axelrod was just trying to prove that he belongs on Chicago's major-league roster.
Axelrod began to prove himself with three innings of one-hit ball in a 9-0 victory over the Dodgers. The White Sox made it look easy. Axelrod and five relievers limited the Dodgers to three hits. The White Sox got 14 hits off seven Dodger pitchers.
"My job is to be there if I'm needed, no matter what happens in spring or the regular season," said Axelrod, who last season was 1-2 in seven starts and 1-0 in seven relief appearance for the White Sox.
Chicago scored two in the third, one in the fourth, two in the seventh and two in the ninth. White Sox catcher Tyler Flowers led the hit parade with home run in the fourth off.
"It was an OK at-bat," said Flowers, who wasn't happy with several pitches he took before sending a 2-3 pitch over the left-field fence. "I didn't really see it well except for a couple of pitches. The result is good, but there is definitely more work to be done."
The Dodgers' three hits came from Juan Uribe with a single, Andre Ethier with a triple and Yasiel Puig with a double. Puig sent a shot to left field in the ninth and rounded first base to second with the power of an NFL linebacker. Then, was nearly thrown out at third
"You wouldn't want to get run over by him," Dodgers manager Don Mattingly said of the outfielder, a Cuban defector who in the off-season signed a seven-year deal for $42 million. "But you want to see that kind of aggressiveness, especially in young guys."