Kershaw struck out five and walked one.
"I felt fine. I'm glad these don't count," Kershaw said.
Chicago leadoff hitter Adam Eaton hit a line drive at center fielder Joc Pederson, who misplayed it, allowing Eaton to circle the bases for an inside-the-park home run.
White Sox right fielder Avisail Garcia hit a three-run home run in the bottom of the sixth inning off the first pitch he saw from Kershaw and finished 2 for 3 with four RBIs.
"There's not much else you can say other than it's time to get going, it's the regular season now," Kershaw said. "It wasn't great, there was some improvement in the middle innings, but obviously that home run didn't help."
Dodgers manager Don Mattingly said he was "OK" with Kershaw's performance on the hill, but he knew his two-time Cy Young award winner wouldn't be.
"I'm sure Kersh is not happy with it," Mattingly said. "I think there were stretches where he would get into a little rhythm and everything was kind of him doing what he wanted to do, and then you could see him throw a ball and not go where he wanted and be frustrated.
White Sox: Tabbed Chicago's opening day starter, Chris Sale pitched 4 1-3 innings Saturday night, allowing two hits and two runs, one earned, while walking two and striking out five. Both runs he surrendered came in the first inning, setting down 10 of the final 13 batters he faced before being removed for Ronald Belisario.
Dodgers: Despite Kershaw's hiccup Saturday night, the reigning Cy Young award-winner will start his fourth consecutive season opener when Los Angeles takes on the Arizona Diamondbacks in Sydney next Saturday.
"Obviously I don't want to have a 9 ERA in the regular season, so I'm going to try not to have that," said Kershaw, who will take an 18-hour flight to Australia with the rest of the Dodgers on Sunday night.
Kershaw is 0-3 with a 9.20 ERA in four starts this spring after becoming the major leagues' highest paid pitcher by signing a seven-year, $215 million deal in January.
White Sox: Second baseman Gordon Beckham injured his left oblique and will be sidelined for at least seven days.
"I was taking a couple of light hacks in the cage after the game yesterday and one swing, I felt it," Beckham said. "It was pretty obvious in terms of just what, I could tell once I took the swing something was wrong."
Dodgers: Matt Kemp took another step toward recovery from a surgery on his left ankle in October, practicing slides onto a padded cushion Saturday.
"I know he was fairly excited today, he got to slide, as far as before the game," Mattingly said. "Today, he was getting two at-bats, and it's going to be a build from there and moving through this next week."
DA WHITE SOX?
Former Chicago Bears coach and Hall of Fame tight end Mike Ditka paid a visit to the White Sox camp on Saturday and threw out the first pitch. Ditka, who led the Bears to the Super Bowl title after the 1985 season, was in town to visit his newly opened Ditka's restaurant in the Vee Quiva Hotel & Casino in nearby Leveen.
USING YOUR HEAD, OR NOT
In the top of the fifth inning, Los Angles third baseman Juan Uribe hit a sharp ground ball to shortstop Alexei Ramirez, who made a diving play to his right and threw from his knees to Marcus Semien covering second base in effort to force out runner Scott Van Slyke.
Van Slyke was called safe, and Semien then tried to throw to first base to get Uribe, but the ball bounced off Van Slyke's helmet and into right field as Justin Turner scored on the play.
Chicago White Sox manager Robin Ventura challenged the safe call at second base, but it was not reversed upon review.