The Colorado Rockies selected Moll in the third round of the 2013 Major League Baseball draft.[3] He made his professional debut with the Low-A Tri-City Dust Devils,[4][5] posting a 1.80 ERA in 30 innings pitched. In July, Moll combined with three other pitchers to throw a no-hitter.[6] He returned to Tri-City in 2014 and appeared in only nine games due to injury. In 2015, he pitched for both the High-A Modesto Nuts and the Double-A New Britain Rock Cats, where he posted a combined 2.63 ERA with 74 strikeouts in 68.1 innings pitched between both clubs. After the season, he pitched in the Arizona Fall League. Moll spent 2016 with the Triple-A Albuquerque Isotopes, where he posted a 3–5 record with a 4.94 ERA.[7] The Rockies added him to their 40-man roster after the season.[8] Moll began the 2017 season with Albuquerque, but was designated for assignment on August 11, 2017.
On August 16, 2017, Moll was traded to the Oakland Athletics in exchange for a player to be named later or cash considerations.[9] Oakland optioned him to the Triple-A Nashville Sounds upon his acquisition.
The Athletics promoted Moll to the major leagues on September 1, 2017, and he made his major league debut that night.[10] He was designated for assignment after the season on November 20.[11]
On November 27, 2017, Moll was claimed off waivers by the Pittsburgh Pirates.[12] After being designated for assignment by Pittsburgh, the Seattle Mariners claimed Moll off waivers on November 30.[13]
On March 17, 2018, Moll was claimed off waivers by the Toronto Blue Jays.[14] He was designated for assignment on March 29,[15] and was assigned outright to the Triple-A Buffalo Bisons after clearing waivers on March 31.[16] In 15 games with Buffalo, Moll logged a 1-3 record and 5.30 ERA.
In the 2018 Winter Meetings, the San Francisco Giants selected Moll from the Blue Jays in the minor league phase of the Rule 5 draft.[17] He was assigned to the Double-A Richmond Flying Squirrels to start the 2019 season, and also pitched for the Triple-A Sacramento River Cats. Between the two teams in 2019, he was 2-2 with 2 saves and a 2.39 ERA in 41 relief appearances covering 49 innings in which he struck out 54 batters.[18] He became a free agent following the 2019 season.[19] He re-signed with the Giants on a minor league contract on January 6, 2020. Moll did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[20] Moll became a free agent on November 2, 2020.
On November 17, 2020, Moll signed a minor league contract with the Arizona Diamondbacks organization.[21] Moll was assigned to the Triple-A Reno Aces to begin the 2021 season. In 21 appearances with Reno, Moll recorded a 5.82 ERA with 30 strikeouts in 21.2 innings of work.
On July 2, 2021, Moll was traded to the Oakland Athletics organization in exchange for cash considerations.[22] The following day, Moll was selected to the active roster.[23] On July 17, Moll made his first appearance with Oakland in 2021, and first MLB appearance since 2017, pitching a scoreless inning against the Cleveland Indians.