Nolasco (6-8), acquired on Saturday in a trade with the Miami Marlins, also doubled and singled, driving in a run and scoring another.
Adrian Gonzalez drove in three runs for Los Angeles, but Hanley Ramirez went zero-for-four, snapping his 19-game hitting streak.
Ian Kennedy (3-5), facing the Dodgers for the first time since serving a 10-game suspension for his role in a bench-clearing brawl a month ago in Los Angeles, allowed six runs, five earned and nine hits in 5-2/3 innings.
He hit Ramirez with a pitch in the first inning.
The Dodgers pulled within 2.5 games of the NL West-leading Diamondbacks.
In other NL action, it was:
‧ Phillies 4, Nationals 2
‧ Brewers 2, Reds 0
‧ Mets 10, Giants 6
‧ Padres 2, Rockies 1
In interleague play, it was:
‧ Cubs 7, Angels 2
‧ Athletics 2, Pirates 1
‧ Cardinals 9, Astros 5