Three weeks into his Major League career, Puig already has five games with at least three hits and 12 with at least two. The Cuban raised his average to .442 and is second on the Dodgers with seven homers.
"I'm surprising everybody," said Puig, who has played just 20 games.
Nick Punto started the rally with a double down the right-field line, moved to third on a sacrifice by Mark Ellis -- who reached on an error by Giants starter Madison Bumgarner -- and scored on Puig's single past shortstop Brandon Crawford.
"He really thrives in the moment," Dodgers catcher A.J. Ellis said of Puig. "It's no secret that he loves the spotlight and being out there on center stage. He's been producing and doing an amazing job."
Hanley Ramirez provided an insurance run with an RBI groundout that scored Ellis. The shortstop went 1-for-4 and is batting .462 with two doubles, three homers and eight RBIs over the past seven games.
The Dodgers' offense had been quiet before that, aside from Puig's solo shot to right in the first.
Puig is 11-for-16 (.688) this season in the first inning, with three extra-base hits. Five of his seven home runs have been to right.
"For him to go the other way his first time seeing [Bumgarner] and hit a home run, it just exudes talent," said veteran Jerry Hairston. "His talent is really second to none. He's fun to watch."
That lead didn't last long, though, as the Giants tied it in the top of the second on Andres Torres' double down the left-field line. Jerry Hairston was unable to field the ball cleanly in the corner, which allowed Joaquin Arias to score from first. But Arias was injured on the play and was removed from the game due to a strained left hamstring.
Bumgarner settled in after Puig's homer and retired 16 of the next 17 Dodgers, including 11 straight after walking A.J. Ellis to lead off the third, until Puig singled through the right side in the sixth.
"He's hot right now," said Bumgarner, charged with three runs (two earned) on five hits in seven-plus innings. "He's been hot since he's been here. When he's getting something to hit, I don't think he's missing it."
Meanwhile, Dodgers starter Hyun-Jin Ryu worked out of trouble for much of his outing and was charged with one run on eight hits in 6 2/3 innings. Ryu has allowed 26 hits in three starts against the Giants.
But Ryu made pitches when he needed to and kept the Dodgers in the game.
The Giants loaded the bases against Ryu with two out in the third, but the left-hander got Crawford to fly out to end the threat. In the fifth, Ryu got Crawford to bounce into a double play to escape another bases-loaded situation. The Dodgers caught a break one batter earlier, when Giants catcher Buster Posey tripped over third base and failed to score on a single by Pablo Sandoval.
"He really grinded tonight; it was a real battle for him," A.J. Ellis said. "They really battle him hard. For him to hang in there and only give up one run, it says a lot of what he's all about and the kind of competitor he is."
The Dodgers escaped trouble again in the seventh, when Ronald Belisario relieved Ryu and struck out Hunter Pence to end the frame and strand Posey on second. Posey doubled to right on a fly ball that Puig was unable to catch at the wall. As Puig backed into the chain-link fence that covers the scoreboard embedded in the wall, his glove jerked and the ball bounced off the fence.
The Dodgers couldn't capitalize on a scoring chance in the bottom of seventh, as A.J. Ellis grounded out to strand runners on first and second.
But Puig delivered in the eighth and gave the Dodgers their first win over the Giants since Opening Day.
The last time these two clubs met, the Giants swept a three-game series in San Francisco, including two wins of the walk-off variety. This time, the Dodgers returned the favor.
"In tight games, they've seemed to be the ones to end up on top, so it's nice for us to win one of these close ones," said Dodgers manager Don Mattingly.
The Dodgers hadn't won three in a row since sweeping the Pirates at home April 5-7. But with Puig in the mix, Ramirez heating up and Matt Kemp and Scott Van Slyke close to coming off the disabled list, the Dodgers believe more win streaks are on the horizon.
"We're starting to get healthy, which is nice, and as we get healthy, I think that throughout the summer we'll start playing some really good baseball," Punto said.