Dinamo Zagreb Baturina made his debut for
Dinamo Zagreb II on 14 February 2021, when Dinamo's second team lost to
Bijelo Brdo 1–0. He made his debut for
Dinamo Zagreb's first team on 16 May 2021 in the
2020–21 season, in which they defeated
Gorica 3–0. He made his debut in the
Croatian Football Cup on 22 September, when Dinamo defeated
Orient 4–1. Eight days later, he made his debut in the
UEFA Europa League against
Genk, which Dinamo won 3–0. He scored his first goal for Dinamo on 5 March 2022 in a 3–0 victory over
Šibenik. On the final matchday of the
2021–22 season, he scored a goal and provided an assist in a 3–1 win over
Hajduk Split. On 6 September 2022, he debuted in the
UEFA Champions League, in which Dinamo beat
Chelsea 1–0. On 15 July 2023, he scored the only goal in the
Super Cup match against Hajduk Split.
Como On 17 June 2025, Baturina signed a 5-year contract with club
Como. ==International career==