Nolasco (6-8) allowed a run on four hits and struck out five in his first start for Los Angeles since being acquired in a weekend trade from the Miami Marlins.
Adrian Gonzalez backed up Nolasco with three RBI, and Los Angeles won its fifth consecutive games. The Dodgers improved to 11-2 in their last 13 contests and trail Arizona in the NL West by 2 1/2 games.
Martin Prado drove in the only run for the Diamondbacks, who lost for the second time since winning five in a row. Ian Kennedy (3-5) took the loss with six runs – five earned – on nine hits over 5 2/3 innings.