Puig hit a three-run homer and threw out a runner at second base, leading Los Angeles over the Arizona Diamondbacks 4-1 Sunday.
Puig connected with two outs following an intentional walk. He flipped his bat after capping a four-run sixth inning against Josh Collmenter (0-2).
"Obviously it was a big hit by Yasiel," Mattingly said. "I was hoping it would get up. I knew it was going to get us another run, so it was a good feeling right away."
The Diamondbacks walked Adrian Gonzalez with two outs to pitch to Puig.
"It's definitely not an easy choice," Arizona catcher Miguel Montero said. "They've got a good lineup from top to bottom, so you have to think about who you have to pitch around because they're all pretty good hitters."
"I thought it was a good pitch that we made on Puig, but he just put a good swing on it. We wanted to come inside on him," he said.
Puig hit a liner over the fence in left-center. He hit 19 homers last season as a rookie after coming up to the Dodgers in June.
Dodgers starter Josh Beckett pitched five innings of one-hit ball, striking out seven and walking two.
Beckett and some of his teammates have been getting intravenous fluids because of a flu bug that's been going around the clubhouse. He wound up with his third no-decision in three starts, with none of them going past the fifth inning.
The three-time All-Star righty remained winless since Sept. 30, 2012, when he beat Colorado at Dodger Stadium.
Beckett was 0-5 with a 5.19 ERA in eight starts last season before sitting out the final five months because of a groin strain and a subsequent bout with thoracic outlet syndrome, a nerve condition that required him to undergo surgery in July.
"It would have been nice to go a little deeper, especially with how much the bullpen's been used. But I felt like it was probably in the best interest of the team to not keep going," Beckett said.
"I felt like I've done a decent job in my last couple of outings, but I think there's still room for improvement," he said.
Jamey Wright (1-0) got three outs for his 93rd career victory, spread over 19 big league seasons and 10 different clubs.
Kenley Jansen struck out the side in the ninth for his seventh save and fifth against the Diamondbacks.
Beckett threw 83 pitches and allowed only a leadoff single to right field in the second by Miguel Montero. But Montero tried to stretch it into a double and was thrown out by Puig.
"Obviously, I'm not the fastest guy in the world, but he had to make a perfect throw," Montero said. "I could have done a better job going around first base, but I took too wide a turn and lost a couple of steps."
The Dodgers broke through in the sixth after Dee Gordon singled and Carl Crawford had a hit-and-run triple into the right field corner. It was Crawford's first triple of the season and 118th of his career, the most among active players.