Ryu, who was 14-8 with a 3.00 ERA as a rookie last year, didn't have a walk or a strikeout.
"It was good to see us throw up all of those zeros," Dodgers manager Don Mattingly said.
White Sox starter Chris Sale also made his exhibition debut, striking out four in 2 2/3 scoreless innings. He gave up one hit and walked none.
Ryu showed up for camp in better shape than a year ago. He lifted weights in the offseason for the first time.
"I know more of what to expect now than I did," Ryu said through a translator. "I actually got my arm in shape before spring training."
Held to two hits over the first six innings by five pitchers, Los Angeles went ahead in the seventh when outfield prospect Joc Pederson hit a two-run homer off Jake Petricka.
Pederson was the Dodgers' minor league player of the year in 2012 and was picked for last year's All-Star Futures game.
First baseman Jose Abreu made his first appearance in a White Sox uniform. The Cuban slugger signed for six years and $68 million in October. He went 0 for 2 against Dodgers pitching, which held the White Sox to five hits.
Chicago manager Robin Ventura said he plans to use several lineups throughout the spring.
"You run it out there and see what it is," Ventura said. "It'll change I think just with putting different guys in there and giving every guy an opportunity at different spots just to see what they can do. That's just the first one."
White Sox: Sale threw 42 pitches, 26 strikes. The only hit he gave up was a double to Adrian Gonzalez in the second inning.
"For the most part I felt like I located my fastball pretty well," the left-hander said. "I threw a couple of good changeups after having a couple of bad ones that just slipped out of my hand. I was able to corral that and get some good work in today."
Dodgers: Ryu threw 30 pitches, 20 strikes. "I'm satisfied with my performance," he said. "I'm more satisfied that I didn't give up any bases on balls and that I had command of my pitches."
White Sox: Nate Jones is recovering from a strained muscle near his lower back. He threw two bullpen sessions within the last week, on Sunday and Wednesday. Jones arrived in camp as the leading contender to be the White Sox closer.
Dodgers: Zack Greinke is expected to miss his next scheduled start, Tuesday against Seattle, because of a strained right calf sustained while throwing just four pitches Thursday. Greinke played catch Friday. Mattingly said the right-hander probably will play catch Saturday. Greinke had been scheduled for a bullpen session that day.
Center fielder Matt Kemp had an MRI on his surgically repaired left ankle Thursday instead of Friday. The Dodgers expect results this weekend. Kemp had microfracture surgery in October.
Left fielder Carl Crawford, scratched Thursday because of a tight left quadriceps, was optimistic about playing Saturday against the Brewers. "There's a little something in there, but sometimes you got to play through it to get it right," he said.
Pitching prospect Ross Stripling is scheduled for an MRI after complaining about pain in his right elbow.
With the uncertainty surrounding Greinke's calf injury, there's a better chance Ryu will start one of the two games the Dodgers play in Australia on March 22 and 23 in a season-opening series against Arizona.
"Whatever the team wants me to do," Ryu said.
But there's one thing he won't do. Ryu was asked if he would try kangaroo meat.
"No," he said.