Manny Ramirez added two RBI in helping the Dodgers improve their record against Eastern Division teams this year to 12-6.
Ramirez singled in a run in the first before Hudson produced his bases-loaded double to give Los Angeles a quick 4-0 lead. Hudson, however, limped off the field in the seventh inning when he was hit in the knee by a pitch from Brian Stokes.
Ramirez had another RBI base hit in the second and Juan Castro singled home two more in the eighth after replacing Hudson.
The beneficiary of the offense was Randy Wolf (4-3), who gave up two runs on seven hits over 6 1/3 innings. It was Wolf's first victory since May 28.
Livan Hernandez (5-5) was roughed up for eight runs on 11 hits in four frames. New York lost for the 10th time in 13 games.
Los Angeles won a series on New York's home field for the first time in five years.
Celebrity Families of 2014 [PHOTOS]