Puig hit his first career grand slam, Zack Greinke pitched four-hit ball over seven innings, and Los Angeles Dodgers won 5-0 on Thursday night, snapping the Braves' five-game winning streak.
"He's definitely stepped right in and come up with some big moments for them," Jason Heyward said.
Cory Gearrin relieved Hudson with the Braves trailing 1-0 in the eighth. Gearrin proceeded to load the bases with one-out singles to Skip Schumaker and Luis Cruz, and a walk to pinch-hitter Hanley Ramirez.
Puig then homered on the first pitch into right field, extending the Dodgers' lead to 5-0. It was the third homer of the week for the 22-year-old Cuban defector who came up from the minors on Monday.
"I've just got to make better pitches," Gearrin said. "I've got to get the ball down more. I'm a ground-ball pitcher. But I'm going to learn from it, go back and look at the video. I know what I need to do."
Puig had singled, struck out and grounded out to shortstop in his three previous at-bats.
Hudson (4-5) dueled Greinke through seven innings, allowing one run and four hits. He struck out five and walked none in losing his fourth consecutive decision since May 10. He's 0-4 in his last six games with a 5.29 ERA.
"It was one of those games where I was making pitches and Greinke was making pitches," he said. "You'd hope that one run wouldn't lose the ballgame for you. But there are going to be games like that."
The NL East-leading Braves lost for the first time in June. They had won seven of nine and 15 of 19 coming into the opener of their seven-game West Coast trip.
Ramiro Pena, hitting .321 coming in, was 1 for 4 with a strikeout. Freddie Freeman, who came in hitting .306, was 1 for 4 with two strikeouts for the Braves. Andrelton Simmons was hitless in four at-bats, snapping his career-high 11-game hitting streak — the longest such run for a Braves hitter this season.
Greinke (3-1) put his recent struggles behind him, striking out a season-high seven and walking three to earn his first victory since May 15 against Washington.
The right-hander had given up four runs and nine hits while walking three in 5 1-3 innings of a 7-6 loss in 10 innings at Colorado last weekend, one of four recent rough outings for Greinke.