Billingsley (4-6) gave up a two-run home run to Derrek Lee in the first inning but retired the next 13 batters. He gave up two runs and four hits over six innings, leaving the game when Manager Joe Torre sent Terry Tiffee to pinch-hit for him to start the seventh inning.
"Chad was great," Torre said. "He's been that way."
The Cubs loaded the bases in the sixth, but Billingsley snagged a comebacker by Kosuke Fukudome that resulted in an inning-ending 1-2-3 double play.
But Ryan Dempster (6-2) limited the Dodgers to a solitary run over seven innings.
"We knew it'd be a good pitching duel and he came out on top," Billingsley said.
The Dodgers' slumping offense wasn't completely devoid of signs of encouragement, as Jeff Kent and Matt Kemp got back on track for at least a day.
Kent, who entered the game with a .143 average in May, was three for four. He reached base on an infield hit in the first inning, though the sequence ended in Juan Pierre's getting caught in a rundown play between third and home. He singled to right in the sixth and to left in the eighth, helping the Dodgers load the bases in both innings.
"He hit the ball hard all four times," Torre said.
Kemp looked clueless in his first at-bat, striking out by swinging at a slider from Dempster that was out of the zone, but he responded by doubling twice and drawing a walk in his final three trips to the plate.
"Matt helped himself at the end," Torre said. "The last couple of at-bats, he certainly had better at-bats."
Hiroki Kuroda climbed out of the Dodgers' dugout and walked behind the cage as the Cubs were taking batting practice, a pack of Japanese reporters on his tail.
Kuroda, who will start today for the Dodgers, didn't walk over to visit countryman Fukudome, but his former teammate, Alfonso Soriano, who played alongside him with the Hiroshima Carp in 1997. Soriano played his first season of professional baseball with the Carp in 1996 as a 20-year-old.
Soriano spent most of his two seasons in Japan on the Carp's minor league team and Kuroda was on the top-level team as a rookie in 1997, but they lived in the same dormitory and their teams often practiced at the same facility.
Japanese reporters who follow Fukudome say that Soriano frequently greets them in Japanese and is heard singing Japanese songs in the clubhouse.
Of Kuroda, Soriano said, "Initially, we didn't spend much time together because I was with the minor league team. But we struck up a friendship. I was very happy to see him here. He's taken his chance to play in the big leagues and I'm happy for him."
Russell Martin will rest today and backup catcher Danny Ardoin, who was called up from triple-A Las Vegas last week, will play in his first big league game of the season. . . . Former Dodgers Manager Tom Lasorda will lead the singing of "Take Me Out to the Ballgame" today at Wrigley Field.