Dmitry Baevsky was born May 24, 1976, in St. Petersburg (then Leningrad), Russia, the only child of a writer and a translator. His great-grandfather, Moisei Beregovsky, was among the most respected Jewish ethnomusicologists of his era, spending his life gathering the melodies and words of Yiddish folk songs and Eastern European klezmer music. Baevsky started piano at six, later discovering alto saxophone as a teenager. In 1991 he entered the Mussorgsky College of Music in St. Petersburg, studying for four years with Russian jazz saxophonist Gennady Goldstein, and performed at jazz venues and international festivals throughout Russia during the 1990s.

At nineteen he moved to New York and was accepted into the New School University's Jazz Department on a full scholarship, remaining an active fixture of the New York jazz scene after graduating. He released his first album as leader, Introducing Dmitry Baevsky (2005, Lineage Records), featuring Cedar Walton and Jimmy Cobb alongside guitarist Ilya Lushtak and bassist John Webber. In 2009 he recorded Some Other Spring (Rideau Rouge/Harmonia Mundi) while touring Europe with guitarist Joe Cohn, and in September 2010 released Down With It on Sharp Nine Records, featuring trumpeter Jeremy Pelt alongside Jeb Patton, David Wong, and Jason Brown. He appeared on trumpeter Bruce Harris's debut album, Beginnings (2017), whose own career is covered in full in his JazzProfiles.com profile.

Baevsky's grounding under Russian jazz saxophonist Gennady Goldstein, combined with his subsequent decades within the New York straight-ahead jazz scene, made him one of the more distinctive alto saxophonists to bring a hard-bop sensibility rooted in Charlie Parker's tradition across an international, Russian-to-American career path.