Twins left-hander Martin Perez was on the mound for both of the triple plays.
With three runs already in for Atlanta in the third inning and the bases loaded on Wednesday, Tyler Flowers hit a sharp grounder straight to third baseman Miguel Sano. He stepped on the bag and threw the ball to second baseman Jonathan Schoop, whose relay to first baseman C.J. Cron was in plenty of time to beat Flowers.
That kept the Braves from building on their 6-0 lead. They ended up winning, 11-7.
"It did buy us a little bit more time and some more pitches and some more innings,'' Twins manager Rocco Baldelli said.
Perez was also pitching on July 22 against the New York Yankees when Edwin Encarnacion grounded into a 5-4-3 triple play turned by Luis Arraez, Schoop and Sano, who was playing first base in that game.
The major league record for most triple plays turned in one season is three, with the Chicago White Sox in 2016 the most recent of several teams to do so.
Before this year's double, the Twins had not turned a triple play since June 1, 2017.
On July 17, 1990, they performed an even rarer feat -- two triple plays in the same game, against the Boston Red Sox.
The Associated Press contributed to this report.