On February 12, 2021, the Marlins traded Hurt and Alex Vesia to the Los Angeles Dodgers in exchange for Dylan Floro.[10] He split his first professional season between the Arizona League Dodgers and the Rancho Cucamonga Quakes, going 2–2 with a 5.57 ERA over 21 innings pitched.[11] After the season, he played in the Arizona Fall League with the Glendale Desert Dogs.[12] He opened the 2022 season with the Great Lakes Loons and was promoted to the Tulsa Drillers in early July.[13] Between the two levels, he pitched in 25 games (19 starts) and finished with a 5–7 record, a 5.27 ERA, and 109 strikeouts over 71+2⁄3 innings.[11] He returned to Tulsa to open the 2023 season.[14] In early August, he was promoted to the Oklahoma City Dodgers.[15] Between Tulsa and Oklahoma City in 2023, he appeared in 26 games (16 starts) with a 4–4 record, 3.91 ERA and 152 strikeouts in 92 innings.[11] He was selected as the Dodgers 2023 Minor League Pitcher of the Year.[16]
On September 12, 2023, Hurt's contract was purchased to the 40-man roster and he was promoted to the major leagues for the first time.[17] In his debut later that day, he pitched two innings of relief against the San Diego Padres, retiring three players on nine pitches in the eighth inning and striking out the side in the ninth. His first MLB strikeout was of Garrett Cooper.[18]
Hurt began the 2024 season out of the Dodgers' bullpen, where he made three appearances and logged a 1.35 ERA.[19] On April 20, 2024, he was placed on the injured list with right shoulder inflammation.[20] He was activated from the injured list on June 21 and optioned to Triple-A,[21] where he pitched 14+2⁄3 innings over 13 games, with two starts, and allowed five earned runs on nine hits for a 3.07 ERA.[11] On July 24, it was announced that Hurt would undergo Tommy John surgery, and miss the remainder of the season.[22]