Bennie Ross Crawford Jr. was born in Memphis on December 21, 1934. He began on piano at nine, playing for his church choir, and picked up the alto saxophone only because he wanted into the band at Manassas High School and his father owned one. The name that stuck came later, at Tennessee State University in Nashville, where bandmates decided he resembled a local saxophonist called Hank O'Day.

Memphis gave him an early start. In 1952, at seventeen, he played on a session for B.B. King alongside Ben Branch and Ike Turner. His hometown contemporaries were Phineas Newborn Jr., Booker Little and George Coleman. At Tennessee State he majored in music, studied theory and composition, played alto and baritone in the Tennessee State Jazz Collegians, and led a rock and roll quartet called Little Hank and the Rhythm Kings on the side. He named Charlie Parker, Louis Jordan, Earl Bostic and Johnny Hodges as his early influences.

Ray Charles heard him at Tennessee State in 1958 and hired him on baritone saxophone. Crawford moved to alto in 1959 and became musical director of the Ray Charles orchestra that year, at twenty-four, holding the post until 1963. The band's output during those years includes The Genius Hits the Road (1960) and Modern Sounds in Country and Western Music (1962), a record that took a Black rhythm and blues singer through Nashville material with strings and a choir and spent fourteen weeks at number one on the Billboard album chart. Writing charts inside that operation was Crawford's education in how a jazz musician reaches a mainstream audience without playing down.

Atlantic signed him as a leader while he was still on the payroll. More Soul was cut on October 7, 1960, arranged by Crawford and Charles together, supervised by Nesuhi Ertegun and engineered by Tom Dowd. Ralph J. Gleason reviewed it in DownBeat as "one of the very best small-band albums in years." Eleven more Atlantic LPs followed through 1970, among them Soul of the Ballad (1963) with the Marty Paich Orchestra, the big-band Dig These Blues (1965) with liner notes by Nat Hentoff, Mr. Blues (1967), and Mr. Blues Plays Lady Soul (1969), an entire album of Aretha Franklin material arranged and conducted by Arif Mardin. Crawford left Ray Charles in 1963 to lead his own septet and kept a working band on the road from then on.

It's a Funky Thing to Do (Cotillion, 1971) marked the turn. In place of his own horn section, the record put him in front of the New York studio players who defined the sound of the decade: Richard Tee, Cornell Dupree, Eric Gale, Chuck Rainey, Ron Carter and Bernard Purdie. One year later Creed Taylor signed him to Kudu, the CTI subsidiary built for records meant to sell.

The eight Kudu albums between 1972 and 1978 are the core of his crossover work. Help Me Make It Through the Night (1972) opened the run with a Kris Kristofferson song, arranged by Don Sebesky and engineered by Rudy Van Gelder. We Got a Good Thing Going (1972) put Bob James on electric piano and George Benson on guitar. Wildflower (1973), recorded across two days that June at Van Gelder's studio with James arranging and conducting, is the album most listeners start with. Don't You Worry 'Bout a Thing (1974) took on Stevie Wonder, and I Hear a Symphony (1975) took on the Supremes and reached number 11 on the jazz chart and number 159 on the pop chart, the highest either figure ever went for him. Hank Crawford's Back (1976), Tico Rico (1977) and Cajun Sunrise (1978) closed the sequence, the last of them the final Kudu release and the only Crawford album on which he sings lead.

After a four-year gap and one album for Buddah with Memphis guitarist Calvin Newborn, he signed to Milestone in 1982 and spent the next eighteen years there. Bob Porter produced nearly all of it, and the band settled into a fixed cast: David "Fathead" Newman on tenor, Howard Johnson on baritone, Dr. John at the piano and organ, Melvin Sparks on guitar and Bernard Purdie on drums. Midnight Ramble (1983) began the run and The World of Hank Crawford (2000) ended it. Alongside those twelve leader dates he made seven co-billed albums with organist Jimmy McGriff, beginning with Soul Survivors (recorded 1980, released 1986) and running through Crunch Time (1998), most of them cut at Van Gelder's studio.

A stroke in 2000 effectively ended his playing career. He passed away in Memphis on January 29, 2009, at seventy-four, from complications of that stroke.

He never had a signature radio hit under his own name. What he had instead was a sound that other saxophonists took as a starting point, most visibly David Sanborn, who named Crawford as the source of his own tone throughout his career and built the 2008 album Here & Gone (Decca, produced by Phil Ramone) around Crawford's music, including his composition "Stoney Lonesome." Sanborn's alto in turn became the default sound of pop and crossover saxophone through the 1980s. Crawford's records also crossed into hip-hop: "Wildflower" is the sample under Kanye West's "Drive Slow," from Late Registration (2005).

Crawford played alto with a wide, vocal, blues-centred tone that owed more to gospel phrasing and Memphis rhythm and blues than to bebop line-running. He named Charlie Parker, Louis Jordan, Earl Bostic and Johnny Hodges as his models, and the Hodges influence is the audible one: long notes, heavy vibrato, melody stated plainly and inflected rather than decorated.

The arranging side of his work is as important as the playing. He wrote charts for Ray Charles before he was thirty, arranged most of his own Milestone records, and thought in terms of section voicings rather than solo choruses. That is why his records sound organised even at their most commercial: the horn writing is doing real work behind the alto.

His crossover records rest on a specific method. Take material the audience already knows, from country songs to Motown to Stevie Wonder, hand it to an arranger who can write for strings and horns, and then play the melody straight with enough blues inflection that it stops being a cover version. He kept improvising throughout, which is the line that separates his Kudu records from the later smooth jazz format they are sometimes filed beside.

His own influence runs through David Sanborn most directly, and through Sanborn into a generation of pop and session alto playing.