"I haven't hit one for a while, so it's great to get back out again," said Puig, who came into the game with a .122 batting average this spring.
"I did feel bad [about the poor spring numbers]. I have been preparing well, but it's not going as well as I'd hoped for. Spring Training, at the end of the day, doesn't matter. It's two months, and the season is long. Those at-bats are the ones that matter."
Manager Don Mattingly seemed to agree, discounting Puig's batting-practice results as well.
"With him, batting practice means pretty much nothing," Mattingly said. "We know Yasiel can hit. The games before we left, he swung OK but didn't get hits.
"I see this as a year of transition for him. We've seen [pitchers] make adjustments and seen him handle the adjustments and make them back. He showed last year he can."
Puig tied the game with a towering two-run shot to left field in the eighth inning off Matthew Williams, scoring A.J. Ellis, who had walked. It was only the second hit of the game for the Dodgers, the other coming from first baseman Adrian Gonzalez, who left after his fourth-inning at-bat with lower back tightness.
The Dodgers took the lead later in the eighth. Chone Figgins followed Puig's homer with a walk, took third when second baseman Logan Wade booted Mike Baxter's routine grounder and scored on catcher Ryan Battaglia's passed ball. Baxter scored on Juan Uribe's single.
The Dodgers went with a lineup that might show up again Opening Night, although Mattingly wouldn't confirm that. It had Dee Gordon leading off at second base, Puig batting second and Scott Van Slyke in left field.
Prospect Zach Lee, the starting pitcher for the Dodgers, allowed one run on three hits with six strikeouts in four innings. Fellow non-roster pitcher Red Patterson allowed one run on two hits with four strikeouts in three innings.
Lee, most likely ticketed to Triple-A Albuquerque this year, said SCG felt like a typical baseball stadium and resulted in "just a normal game."
Lee pitched out of a second-inning jam by getting Logan Wade to bounce out with runners on second and third and two outs, but Australia found the scoreboard in the third inning.
With one out, former Boston prospect Mitch Dening was nicked by a pitch, Brad Harman doubled him to third and Red Sox farmhand Stafan Welch's sacrifice fly to deep right field scored Dening.
Australia scored another run in the sixth inning on a leadoff walk to Harman, a wild pitch, a groundout and a two-out, broken-bat infield single by Mike Walker, who took second on Justin Turner's errant underhand flip to first.
Tim Kennelly then singled to right field, but Puig easily threw out Walker at the plate to end the inning.