Puig, hitless on Wednesday for the first time in his young career, singled in his first at-bat and lined a grand slam to right in the eighth on the first pitch he saw from right-hander Cory Gearrin.
As Puig stepped to the plate, manager Don Mattingly and first baseman Adrian Gonzalez turned to each other in the dugout and joked that Puig would go deep.
"We were kidding, but it doesn't really surprise you," Mattingly said.
Gonzalez and Mattingly weren't the only ones in the Dodgers' dugout who shared that feeling.
"We were all thinking the same thing, we just didn't think it would happen on the first pitch," catcher Tim Federowicz said. "He's a special player."
It was the third multi-hit performance in four games for Puig, who finished 2-for-4 to raise his average to .438. The outfielder has three homers and nine RBIs since making his big league debut on Monday, getting his fourth curtain call in the process and an ice bath from Luis Cruz after the game.
Playing with a renewed energy, the Dodgers improved to 3-1 since Puig's promotion from Double-A.
"I'm very happy that the fans are saying my name and the good thing is the team is winning right now," Puig said through a translator.
In just four games, Puig has proven his worth to the Dodgers and his teammates. He had two hits in his debut, capping a 2-1 win over the Padres with a bullet from right field to first base to double off Chris Denorfia. On Tuesday, Puig homered twice and drove in five runs to lead the Dodgers to a 9-7 victory.
"I feel like he feels he belongs here and he's just proving it right now," said Greinke, who saw Mike Trout bring a similar energy to the Angels last season. "I don't think in his mind he's worried about the pitcher being better than him. He feels he belongs."
Puig's latest heroics even drew a reaction from Matt Kemp, who is rehabbing a right hamstring strain in Arizona.
After the grand slam, Kemp tweeted: "That boy is a beast!!!! #puig"
For Greinke, it was the strongest he has looked in five starts since returning from a broken left collarbone three weeks ago.
"It was definitely big for me," said Greinke, who struck out seven and allowed just four hits. "I've been struggling. But I felt like I've been kind of close. It's still not exactly where I want to be, but it was definitely a fun start."
Just as important, the right-hander's deepest outing of the year helped ease the burden on a bullpen that had worked 11 2/3 innings combined over the last three games.
"It kind of allows us to reset our 'pen with Zack being able to work his way through the seventh," Mattingly said. "That was huge for us tonight."
Greinke needed 60 pitches to get through three innings, but settled in and cruised through three more until he encountered trouble in the seventh.
Freddie Freeman and Brian McCann led off the frame with singles, putting runners on the corners. Greinke battled Dan Uggla, eventually striking out the second baseman. Ramiro Pena lined out to left and Scott Van Slyke's quick throw home kept Freeman at third. Greinke then got B.J. Upton to fly out to right to end the threat.
"He's Zack Greinke, he got paid for a reason," Braves outfielder Jason Heyward said. "He has five above-average pitches. He's got his fastball -- four-seam and two-seam -- he's got his cutter, he's got a good changeup, he's got a curveball and he makes his pitches when he needs to."
Braves starter Tim Hudson, meanwhile, gave the Dodgers fits. The veteran allowed four hits in seven innings, allowing just one run on Skip Schumaker's RBI groundout in the second inning. Hudson struck out five and walked none.
Schumaker drove in Van Slyke, who singled to lead off the inning and moved to third on a double by Andre Ethier.
Hudson settled in after that, and didn't allow another baserunner until Adrian Gonzalez singled to lead off the seventh.
Kenley Jansen relieved Greinke to start the eighth and fired a scoreless inning, thanks to a heads-up defensive play as the Dodgers doubled off Jordan Schafer at first base on a fly ball to center.
Schumaker and shortstop Nick Punto faked like they were fielding a ground ball on a long fly by Andrelton Simmons and Schafer slid into second base, then didn't touch second on his way back to first.
Schumaker extended his hitting streak to a career-high 13 games with a single in the eighth. Cruz followed with a single and Hanley Ramirez drew a walk to set the stage for Puig's grand slam.
With Greinke back on track, Kemp and catcher A.J. Ellis scheduled to come off the disabled list in two weeks and Puig providing a spark, the Dodgers feel they are on the verge of turning their season around after two disappointing months.
"We've got a good club and we've got a chance to make some real noise, if we can just get our guys back and get some rhythm going," Mattingly said. "Then you add [Puig] into the mix. It's just dynamic."