Stowers made his professional debut with the Low–A Aberdeen IronBirds. He did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[8] He started 2021 with Aberdeen before being promoted to the Double–A Bowie Baysox.[9] He was later promoted to the Triple–A Norfolk Tides.[10] Over 124 games between the three teams, he slashed .278/.383/.514 with 27 home runs and 85 RBI.[11] After the season, he played in the Arizona Fall League for the Mesa Solar Sox.[12] Stowers started the season with Triple-A Norfolk.
Stowers replaced Brett Phillips on the team's 40-man roster when his contract was selected from the Tides two months later on August 19.[17] His first-ever MLB home run was a two-out 0–2 pitch off Liam Hendriks which he sent to the bleachers in center field in the bottom of the ninth to tie at 3–3 an eventual eleven-inning 4–3 Orioles victory over the Chicago White Sox at Camden Yards six days later on August 25. Two pitches earlier, he had hit what was a potential game-ending foul out down the left-field line which was muffed by Adam Engel.[18]
In 2023, Stowers played in only 14 games with the Orioles, going 2–for–30 (.067) with no home runs or RBI. The rest of his year was spent in the minors, where he missed two months of the season with shoulder inflammation.[19]
In 2024, despite a strong spring training that saw him hit .256 with 7 home runs and 14 RBI, Stowers was optioned to Triple–A Norfolk to begin the year.[20] He surpassed Christian Walker for most career home runs in Orioles minor-league affiliate history with three in a 26–11 away win over the Charlotte Knights on April 3.[21] He also went 4-for-7 with three runs scored and 7 RBI.[22] Two weeks after his recall by the Orioles on May 13,[23] he established an MLB-career-high four RBI with three hits including two doubles in an 11–3 home win over the Boston Red Sox on May 27.[24] In 19 games for Baltimore, Stowers hit .306/.297/.500 with one home run and nine RBI.