In April 2013, Peralta signed a contract as an international free agent with the Seattle Mariners. That year, he made his professional debut with the Dominican Summer League Mariners, where he played the entire season, finishing 3-3 in 13 games (ten starts) with a 1.46 ERA. He pitched for the Arizona League Mariners in 2014, going 1-6 with a 5.29 ERA in 12 appearances. He went back to the Mariners in 2015 and went 2-3 in 11 games (nine starts) with a 4.11 ERA.

Adam Lind was acquired by the Mariners on December 9, 2015, in exchange for Peralta, Daniel Missaki, and Carlos Herrera from the Milwaukee Brewers.[2][3] He pitched to a combined 4-4 record and 3.62 ERA in 82 innings thrown during his time in 2016 with the Wisconsin Timber Rattlers and the Biloxi Shuckers.
Peralta pitched in 2017 for both Biloxi and the Carolina Mudcats.[4][5] Between the two clubs, he was 3-8 with a 2.63 ERA and 1.16 WHIP in 25 games (19 starts).[6] Following the season, the Brewers added him to their 40-man roster.[7] Prior to the 2018 season, Peralta was Milwaukee’s tenth-ranked prospect according to MLB.com.

2018 saw Peralta start with the Colorado Springs Sky Sox. On May 13, he was called up to Milwaukee to make his Major League Baseball debut. That same evening at Coors Field, he made his debut against the Colorado Rockies. In 5.2 innings, he struck out 13 batters and allowed no runs to be scored, breaking the Brewers franchise mark for strikeouts by a first-time starter. He was 6-4 with a 4.25 ERA for the season. With 30 or more innings pitched, he kept right-handed batters to the lowest batting average (.110) among all MLB pitchers.[9] Peralta made 39 appearances for the Brewers in 2019, going 7-3 with a 5.29 ERA and 115 strikeouts in 85.0 innings of work.

Peralta and the Brewers reached a five-year, $15.5MM contract deal on February 28, 2020.[10] Peralta pitched to a 3-1 record and a 3.99 ERA in 15 appearances with the Brew Crew in 2020, striking out 47 batters in 29.1 innings pitched. With 195 strikeouts in 144.1 innings pitched, Peralta pitched to a 10-5 record and a 2.81 ERA in 28 games for the Brewers in 2021.
Due to a lat injury, Peralta was placed on the 60-day injured list on June 14, 2022.[11] He became operational on August 3.