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 and picked up the alto saxophone as a teenager, quickly discovering it as his real calling. In 1991 he entered the Mussorgsky College of Music in St. Petersburg, studying for four years under Russian jazz saxophonist Gennady Goldstein and performing at jazz clubs and international festivals throughout Russia during the 1990s.

His path to the United States began in 1994, when American musicians Jeff Holmes and Bruce Krasin — both connected to the University of Massachusetts Amherst — heard the eighteen-year-old Baevsky play at St. Petersburg's White Nights Festival and invited him to the Jazz in July program in Amherst, where he studied with Holmes as well as NEA Jazz Masters Billy Taylor and Yusef Lateef. He spent a semester at Greenfield Community College in Massachusetts sharpening his English before moving on to New York, where he was accepted into New School University's Jazz Department on a full scholarship. Between 1996 and 1999 he studied there with bassist Buster Williams, trombonist Benny Powell, and drummer Joe Chambers, and remained an active fixture of the New York jazz scene long after graduating — including two decades of appearances at Smalls, one of the scene's defining rooms.

He released his first album as leader, Introducing Dmitry Baevsky (Lineage Records, recorded January 2004 and issued in 2005 as one of the label's first releases), featuring Cedar Walton on piano and Jimmy Cobb on drums alongside guitarist Ilya Lushtak and bassist John Webber. In 2009 he recorded Some Other Spring (Rideau Rouge) with guitarist Joe Cohn, bassist Clovis Nicolas, and drummer Luca Santaniello while touring Europe with Cohn. In September 2010 he released Down With It on Sharp Nine Records, featuring trumpeter Jeremy Pelt alongside pianist Jeb Patton, bassist David Wong, and drummer Jason Brown — a record that stayed on the JazzWeek charts for more than four months. His second Sharp Nine date, The Composers (2012), paired him with pianist David Hazeltine, guitarist Peter Bernstein, bassist John Webber, and drummer Jason Brown for a program built entirely around jazz composer-pianists.

Around 2016 Baevsky relocated to Paris with his French wife, Marina Chassé — herself a jazz artist manager, running the Like a Sound agency — and their son. He has since described the move as creatively clarifying even as it separated him from the New York scene that shaped him. The Paris years opened a new chapter on the independent Jazz Family label: Over and Out (2015) and The Day After (2016), both reuniting him with bassist David Wong and drummer Joe Strasser. In between, Somethin' Special (2016, Blau Records) was recorded in Barcelona with a local rhythm section of pianist Fabio Miano, bassist Ignasi González, and drummer Joe Strasser.

Baevsky has also built a long-running duo partnership with pianist Jeb Patton, a friend from his earliest New York years whom he has described as sharing his vision of jazz as a meeting point of tradition and modernity; their album We Two (2018, Jazz&People), recorded in Amiens, France, showcases that partnership directly, including material drawn from Charlie Parker's less-covered repertoire. Patton and Baevsky are also both members of The New York-Paris Reunion Quintet, alongside trumpeter Joe Magnarelli, bassist Fabien Marcoz, and drummer Bernd Reiter, documented on Live at the Bird's Eye Jazz Club, Basel (2020, Albore Jazz).

His most recent leader albums have appeared on the Barcelona-based Fresh Sound New Talent label: Soundtrack (2021), with Patton, Wong, and drummer Pete Van Nostrand; Kids' Time (2022), a pianoless trio session with bassist Clovis Nicolas and drummer Jason Brown featuring a guest appearance by trumpeter Stéphane Belmondo; and Roller Coaster (2024), reuniting him with guitarist Peter Bernstein, bassist David Wong, and drummer Jason Brown for a program of Benny Golson, Duke Ellington, Ray Charles, and Tommy Flanagan material alongside originals.

Alongside his own leader dates, Baevsky has a substantial sideman résumé: he appears on guitarist Joe Cohn's Restless (2007, Arbors Records), pianist Ehud Asherie's Organic (2010, Posi-Tone), Jeb Patton's Shades and Tones (2015, Cellar Live), pianist Laurent Courthaliac's Woody Allen tribute All My Life (2016, Jazz&People), and trumpeter Bruce Harris's debut album, Beginnings (2017, Posi-Tone), whose own career is covered in full in his JazzProfiles.com profile. On Beginnings, Baevsky shares horn duties in a rotating cast alongside tenor saxophonists Grant Stewart, Andy Farber, and Jerry Weldon — the same Grant Stewart whose own career is profiled separately on JazzProfiles.com; the two saxophonists are labelmates-in-passing on that record rather than co-leaders of any project of their own.

Critical reception has followed Baevsky closely on both sides of the Atlantic. Hot House Jazz's Seton Hawkins praised his "gorgeously dark and warm alto tone," The New York City Jazz Record's Russ Musto called him an "important new voice" with a "robust sound, acute harmonic mind and keen sense of rhythm," and JazzWax's Marc Myers made a similar case for him as a player "distilling the jazz tradition" for a contemporary audience. French outlets have been equally enthusiastic since his move to Paris, with TSF Jazz describing him as a "revelation of the alto saxophone."

Baevsky's grounding under Russian jazz saxophonist Gennady Goldstein, combined with formative New York study alongside Buster Williams, Benny Powell, and Joe Chambers, gave him a hard-bop and bebop vocabulary built on the alto lineage of Charlie Parker, Johnny Hodges, and Benny Carter — the three saxophonists he has named as his deepest influences. His tone is frequently singled out by critics as unusually dark and full-bodied for the instrument, closer at times to a tenor's weight than to the brighter, lighter sound many alto players favor; that combination of harmonic sophistication, "irrepressible swing," and a gift for ballads has made him one of the more distinctive voices to bring a hard-bop sensibility across an international, Russian-to-American-to-Parisian career path. His duo work with Jeb Patton and his membership in The New York-Paris Reunion Quintet also point to a musician drawn as much to close, long-running creative partnerships as to any single fixed band.