Billingsley (7-3) opened the season with five straight victories before dropping two out of three.
He got back in the groove against the Diamondbacks by holding them to four hits and striking out nine over six innings.
Ronald Belisario gave up a two-out single in the seventh and Ramon Troncoso escaped trouble in the eighth when Miguel Montero grounded into an inning-ending double play with runners on first and third.
Jonathan Broxton worked a perfect ninth for his 13th save.
Los Angeles won its second in a row and improved to 25-9 against opponents from its own division.
The game's only run came in the sixth when starter Jon Garland (4-5) allowed a lead-off triple to James Loney and a sacrifice fly to Casey Blake.
Copyright 2009 by United Press International.
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