Hanley Ramirez tied a season high with four hits and drove in two runs during as the Dodgers increased their NL West lead to 3 1-2 games over the idle San Francisco Giants with their fourth straight win. Juan Uribe and Carl Crawford homered for Los Angeles.
Kershaw (18-3) reduced his major league-best ERA to 1.67, allowing three runs - one earned - and three hits while striking out eight in eight innings.
The Padres scored two unearned runs against the to-time NL Cy Young Award winner in the sixth on Rene Rivera's routine flyball to center field that resulted in throwing errors by Puig, catcher A.J. Ellis and shortstop Ramirez - on the same play.
Kershaw is 15-1 with a 1.20 ERA and six complete games in his last 18 starts, including a no-hitter. He has a chance to become the first Dodgers starter to finish with an ERA under 2.00 in consecutive seasons since Sandy Koufax (1963-64).
Odrisamer Despaigne (3-6) was charged with seven runs - six earned and eight hits in 4 1-3 innings.
The Dodgers staked Kershaw to a 2-0 lead with an RBI single by Ramirez in the first, and an opposite-field drive by Uribe in the second inning.
The Padres, whose six-game losing streak is their longest of the season, got one of the runs back in the fourth with Rene Rivera's RBI single. But the Dodgers extended their margin to 4-1 in the bottom half.
Puig drove in Matt Kemp with a single for his 60th RBI and first since Aug. 15. Two batters later, Ellis snapped an RBI drought of 31 at-bats when he grounded to second with the infield in.
The Dodgers blew it open with four in the eighth. Matt Kemp chased Despaigne with an RBI double that extended his hitting streak to 14 games. Crawford then greeted Frank Garces with his seventh homer, a three-run shot that made it 8-1.
Padres: SS Everth Cabrera, who hasn't played since Aug. 9 because of a left hamstring strain, could be activated during next weekend's series in Arizona. He was arrested Wednesday morning on suspicion of driving under the influence of marijuana. ... Neither Joaquin Benoit nor Blaine Boyer, both experiencing shoulder problems, were available out of the bullpen.
Dodgers: Reliever Paco Rodriguez (elbow) continued to throw on flat ground and is scheduled to have a bullpen session in a couple of days.
Padres: Andrew Cashner (2-7, 2.39 ERA) is 0-5 in his last 10 starts despite a 2.90 ERA during that stretch. The team's opening day starter has had his season interrupted by two stints on the disabled list - the first because of a sore elbow that sidelined him for more than three weeks, the second due to a sore shoulder that kept him on the shelf for over two months. Cashner hasn't allowed a home run in 46 career innings against the Dodgers, encompassing five starts and 11 relief appearances.
Dodgers: Roberto Hernandez (8-10, 4.00 ERA) allowed four homers last Monday in a 6-4 loss to Washington. He is 2-2 with a 4.61 ERA in five starts since he was acquired from Philadelphia on Aug. 7.