Playing in his second Major League game, Puig went 3-for-4 with five RBI and scored two runs.
Tim Federowicz added a two-run home to the Dodgers' 10-hit attack and Luis Cruz had an RBI double. J.P. Howell (2-0) earned the win in relief. Brandon League set the Padres down in order in the ninth for his 13th save.
The Dodgers trailed 5-2 early but took control with four runs in the fifth inning and three more in the sixth.
The win was the second in a row for the Dodgers. San Diego lost its third straight contest. Tyson Ross (0-2) allowed three runs on four hits over 2 1/3 innings of relief to absorb the loss.