Smith, the Dodgers' No. 8 prospect, finished 2-for-4 with four RBIs and is hitting .378 in the AFL, while Peters (Dodgers' No. 17) hit his first homer in Arizona after blasting 27 during the regular season.
"I'm just seeing the ball and putting the barrel on it and the hits are falling for me," Smith said. "I'm just trying to keep seeing the ball well and put good swings on it."
Smith wasted no time getting his big day started as he capped a four-run first with a two-run double to extend his hitting streak to five games.
Glendale's offense jumped all over Max Fried (Braves' No. 9), who entered the game with a 0.47 ERA over his first four starts, as each of the first five batters reached base.
The first two scored via an RBI groundout and a bases-loaded walk before Smith drove in a pair with a double to center field.
"It's always nice to get off to that quick start, especially as the road team," Smith said. "We put together some good at-bats in that first inning."
Fried settled down and retired 10 of the next 11 batters he faced before giving up a solo homer to Peters.
"We see that everyday, it's incredible," Smith said of Peters' power.
Although Peoria, which began the day with a league-leading .296 team batting average, boasts a potent offense, Glendale's early runs were more than enough for Brandon Waddell.
The Pirates' No. 23 prospect, who came out of the bullpen in each of his first six AFL appearances, spun a gem in his first start as he fired three scoreless frames.
Waddell threw 22 of his 32 pitches for strikes and gave up just one hit as he lowered his Fall League ERA to 1.50.
"He's pretty good," Smith said. "He had all four pitches working, he was locating the ball and keeping them off balance."
With the game already seemingly in hand, Smith came up in another big spot in the fifth and put the game out of reach with a two-run single.
The strong offensive showing in Arizona is a positive development for Smith, who hit just .232 in 72 games with Class A Advanced Rancho Cucamonga and has hit .238 over the entirety of his professional career.
"There's always adjustments, but it's just more confidence now than anything," Smith said. "[During] that time off, I really studied some video to learn what I was doing wrong, what I wasn't and made those quick adjustments."
Peoria couldn't put together enough offense to come back, but the club did avoid a shutout as Ronald Acuna (Braves' No. 1, MLB No. 5) and Lourdes Gurriel (Blue Jays) each hit solo homers in the eighth.
William Boor is a reporter for MLBPipeline.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.