Billingsley (9-5) got the win with six strong innings and left it up to Kuo and Broxton to stifle the NL West-leading Padres the rest of the way.
Billingsley scattered three hits and struck out four for his second consecutive shutout win. Kuo struck out five in two innings and Broxton retired the Padres in order in the ninth for his 20th save.
Andre Ethier came off the bench to hit for Billingsley in the seventh and singled to drive in both Los Angeles runs and give the Dodgers the win in the first of three big games between the division rivals.
Jon Garland (9-7) took the loss despite a respectable 6 2/3-inning start. Garland allowed two runs on five hits and fanned five. Garland and three relievers held Los Angeles to five hits.
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