Acuña, 20, became the youngest player in the live ball era (since 1920) to homer in four straight games.
"I just found out,'' he said through an interpreter when asked if he knew about his unique accomplishment. "I give thanks to God for the opportunity to make history in my own sense.''
Acuña hit an opposite-field drive into the Braves' bullpen in Game 1, powering Atlanta to a 9-1 victory. It was more of the same in the nightcap, when he sent a towering shot into the seats in left-center, sparking the Braves to a 6-1 win.
"It's pretty special,'' said Braves star Freddie Freeman, who also homered in Game 2. "He's some kind of hot right now. What he's doing at the plate, you just don't see it very often.''
Acuña appears to be only the fourth player in baseball history to hit a pair of leadoff homers in a doubleheader. Two of the others, Rickey Henderson and Harry Hooper, are in the Hall of Fame.
Before that, it was accomplished by Oakland's Henderson at home against the Cleveland Indians on July 5, 1993, and by Hooper while he played for the Boston Red Sox on May 20, 1913, during a pair of games at the Washington Senators.
"Freddie and I were just kind of standing there smiling at each other like, 'Again?'" Braves manager Brian Snitker said. "It's been fun to watch.''
Acuña has flourished since moving into the leadoff role for the Braves. Over the course of about nine hours, he went 5-for-8 with two homers, five RBIs, five runs, two walks and a stolen base.
Acuña has 17 homers this season, four of them leading off games, and is making a bid to be the National League's top rookie despite missing a month with a left knee injury. He currently has 39 RBIs in 259 at-bats.
Information from The Associated Press was used in this report.