Chris Capuano pitched three innings of hitless relief to steady the ship for the Dodgers after starting pitcher Hyun-jin Ryu had surrendered six hits and four runs in the opening stages.
Carl Crawford had a three-run homer while four other players had two RBIs on a big night for Los Angeles at the plate.
The Pittsburgh Pirates also went 2-1 up in their series as they claimed a 5-3 win over the St Louis Cardinals.
Carlos Beltran's home run for the Cards levelled the scores at three at the top of the eighth but the Bucs responded with singles from Pedro Alvarez and Russell Martin to claim the win.
Beltran had a hand in all three of St Louis' runs while Martin and Marlon Byrd both claimed a pair of RBIs for the home side.