"I wish I could throw that curve ball," added Danks of the three-time National League Cy Young Award winner and reigning NL Most Valuable Player Award winner.
Kershaw struck out Micah Johnson looking to open his first 2015 Cactus League appearance, and then struck out Jose Abreu looking with the curve. In the second inning, Kershaw induced two weak ground balls and struck out Conor Gillaspie to end his afternoon.
Danks allowed a Joc Pederson single and a Darwin Barney double to begin the game, then retired the next six hitters to complete his outing. Danks has been focusing on a lower arm angle and a lower leg kick, which he employed to his liking in this 32-pitch, 21-strike effort.
Yasiel Puig (first-inning groundout) and O'Koyea Dickson (sixth-inning RBI double) each drove in a run for the Dodgers. Kyle Jensen added a two-run homer to right field in the eighth, and Scott Schebler roped a two-run double to right-center in the ninth to close out L.A.'s scoring.
The White Sox got singles from Abreu and Alexei Ramirez, who each had two hits in Wednesday's spring opener, and Courtney Hawkins drilled a solo homer off the batter's eye in center field in the ninth inning to put Chicago on the board.
Hawkins is one of the top White Sox prospects getting a look at big league camp, as is Tim Anderson, who singled in the ninth inning but also made two fielding errors at shortstop.
"Bat-wise, he's probably further ahead than he is defensively, but again, he's got good tools," said manager Robin Ventura of Anderson. "So I think for him, [defense] is always going to be something to work on, and we feel he's got the ability to work on it, because he's got some tools."
Up next: Carlos Rodon, the White Sox top-ranked prospect and 14th overall in Major League Baseball per MLB.com, makes his Cactus League debut Friday in a start against the Padres in Peoria at 2:05 p.m. CT, live on Gameday Audio. The southpaw is taking the Cactus League rotation spot of Chris Sale, who is sidelined until at least March 21 with an avulsion fracture in his right foot. Zach Duke and Matt Albers also are scheduled to pitch.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.