Billingsley, likely to be the Dodgers' No. 2 starter behind Cy Young winner Clayton Kershaw, gave up only a single to Alexei Ramirez.
Led by prospect Scott Van Slyke's two-run homer, the Dodgers scored five times in the sixth off White Sox prospect Nestor Molina, acquired in the offseason trade that sent closer Sergio Santos to Toronto. Van Slyke is the son of former major leaguer Andy Van Slyke.
Ramirez had two hits and drove in a run.