Dobzanski was selected by the St. Louis Cardinals in the 29th round, with the 885th pick, of the 2014 Major League Baseball draft.[4][5] He signed with the Cardinals, forgoing his commitment to play college baseball at the University of Louisville.[6][7] He made his professional debut that year with the Rookie-level Gulf Coast League Cardinals, going 2–1 with a 2.67 ERA over 27 innings.[8] In 2015, he pitched for the Johnson City Cardinals of the Rookie-level Appalachian League, compiling a 1–1 record and a 3.94 ERA over 16 innings, and in 2016, he played with the State College Spikes of the Low–A New York–Penn League, going 4–6 with a 3.93 ERA over 14 games (13 starts), striking out 37 batters over 71 innings.[9] In 2017, he spent the season with the Peoria Chiefs of the Single–A Midwest League, going 2–5 with a 3.70 ERA over 31 games (12 starts); he was moved from the starting rotation to the bullpen midway through the year.[10]
Dobzanski began the 2018 season back with Peoria (with whom he was named an All-Star) before being promoted to the Palm Beach Cardinals of the High–A Florida State League in July.[11][12] Over 42 relief appearances between the two clubs, he compiled an 8–4 record with a 2.41 ERA. In 2019, he split time with Palm Beach (earning Florida State League All-Star honors), the Springfield Cardinals of the Double–A Texas League, and the Memphis Redbirds of the Triple–A Pacific Coast League; over 57 relief innings pitched between the three teams, he went 3–3 with a 2.84 ERA and 66 strikeouts.[13] Dobzanski did not play a minor league game in 2020 due to the cancellation of the minor league season caused by the COVID-19 pandemic.[14] On November 2, 2020, he elected free agency.[15]
On January 12, 2021, Dobzanski signed a minor league contract with the Washington Nationals organization.[16] For the 2021 season, he was assigned to the Harrisburg Senators of the Double-A Northeast with whom he went 1–1 with a 3.47 ERA and 46 strikeouts over 46+2⁄3 innings.[17] Dobzanski elected free agency following the season on November 7.[18]
