Sullivan Joseph Fortner was born on December 29, 1986, in New Orleans and began playing the piano at the age of four. His mother directed the choir at a Baptist church, and at seven he started playing the organ there; he has said that he was drawn to the instrument by watching a woman play organ at a local church. For some years he leaned on his perfect pitch to pick up music by ear, a habit that stopped being enough when he auditioned for the New Orleans Center for Creative Arts. He went on to earn a bachelor's degree at the Oberlin Conservatory of Music and a master's degree at the Manhattan School of Music.

His earliest recorded credits include trumpeter Theo Croker's self-released The Fundamentals (2007) and In the Tradition (2008), and Excitable (2009), a Detroit Jazz Musicians Co-Op album led by the trumpeter Marcus Belgrave. In 2009 he was in vibraphonist Stefon Harris's band, including a tour of Europe. From 2010 to 2017 he was the regular pianist in Roy Hargrove's quintet. In 2011 he came under the influence of Barry Harris, after concluding that his knowledge of the music was too shallow. In 2013 he recorded with the Hargrove band's saxophonist Justin Robinson on Alana's Fantasy, a Criss Cross date in memory of the bassist Dwayne Burno, and in 2015 he won the American Pianists Association's Cole Porter Fellowship in Jazz, a prize that carried $50,000, a recording opportunity with Mack Avenue Records and two years of career development.

His debut as a leader, Aria, was recorded at Avatar Studios in New York on November 14 and 15, 2014, and released on Impulse! in 2015 with a quartet that included saxophonist Tivon Pennicott, bassist Aidan Carroll and drummer Joe Dyson; DownBeat gave it four stars. In 2016 he received the Lincoln Center Award for Emerging Artists and a place in DownBeat's "25 for the Future." Moments Preserved (Impulse!, 2018), recorded June 29 and 30, 2017, with bassist Ameen Saleem and drummer Jeremy "Bean" Clemons, brought Hargrove in on trumpet and flugelhorn for part of the program; Hargrove passed away on November 2, 2018. The same year he played on several tracks of Paul Simon's In the Blue Light and made the duo album The Window (Mack Avenue, September 28, 2018) with the singer Cécile McLorin Salvant, which won the Grammy for Best Jazz Vocal Album at the 2019 ceremony. He had already played on one track of her Dreams and Daggers (2017), and he returned as one of two pianists, with Aaron Diehl, and as a co-producer on Ghost Song (Nonesuch, 2022). He is also credited on her With Every Breath I Take (2026), and in July 2024 he was at the piano in her quartet at Norway's Kongsberg Jazzfestival.

Beyond Salvant's records he worked with a wide range of singers and bandleaders: pianist on Peter Bernstein's live quartet album What Comes Next (Smoke Sessions, 2020), on Bruce Harris's Soundview (2021) and on Melissa Aldana's Blue Note debut 12 Stars (2022), and in a duo with the bassist Rufus Reid, whose 2018 sessions came out as Always In The Moment on Newvelle in 2020 and, expanded, as It's The Nights I Like on Sunnyside in 2023. For Samara Joy's A Joyful Holiday (Verve, October 27, 2023) he played piano and organ and sang a duet with her on "Twinkle Twinkle Little Me," which won the Grammy for Best Jazz Performance at the 2025 ceremony. His double album Solo Game (Artwork Records, November 2023) was recorded in two parts: a first disc made in 2021, which he produced with Cécile McLorin Salvant as co-producer, and a second disc recorded in June 2022 and produced by Fred Hersch. Across the set he plays piano, Hammond B3, Fender Rhodes, vibraphone, celesta, Moog, vocoder, drums and percussion.

On July 8, 2023, before one night of a week at the Village Vanguard, he recorded Southern Nights at Sear Sound in New York with bassist Peter Washington and drummer Marcus Gilmore, working without edits or retakes in what was the trio's first run of performances together. Artwork Records released it on February 14, 2025, and it won the Grammy for Best Jazz Instrumental Album at the 68th Annual Grammy Awards on February 1, 2026, bringing his total to three Grammy Awards. In 2025 he also made a duo album with Kurt Elling, Wildflowers, Vol. 1 (Edition Records, recorded August 26, 2024), and an ACT duo record with Croker, Play, which the two produced together. In 2026 he received The Gilmore's Larry J. Bell Jazz Artist Award, and in August of that year he released Leave That In There on Artwork, a trio recording with bassist Tyrone Allen II and drummer Kayvon Gordon, produced by Derrick Hodge and Jack DeBoe.

Fortner is a pianist with a very large vocabulary of touch and texture who sounds as comfortable accompanying a singer as leading a trio. A Variety review of The Window observed that in a voice-and-piano duo he can sound like two bands playing at once, and his long run as an accompanist (Hargrove, Salvant, Joy, Elling) shows in how closely he follows a singer's phrasing. His church-organ beginnings and New Orleans upbringing surface repeatedly: the title track of Southern Nights is the Allen Toussaint song, played with a New Orleans lilt, and on Solo Game and The Window he uses organ, Rhodes and percussion as well as the piano. The harmonic and rhythmic language underneath is bebop and post-bop: Barry Harris was a strong influence from 2011, Thelonious Monk is a clear presence on Southern Nights (an original called "9 Bar Tune" and a reharmonized "Waltz for Monk"), and the trio also plays pieces by Clifford Brown ("Daahoud") and Woody Shaw ("Organ Grinder"). DownBeat rated Southern Nights four and a half stars and Jazzwise gave it four.