The droll, sleek-haired saxophonist Lou Donaldson, who has died aged 98, was disinclined to let a good lick or a good gag wither on the vine. Alongside his immense saxophone eloquence, he possessed a highly entertaining strangled-parrot blues voice, and at gigs in his later years would regularly deliver his vocal party piece, Whisky Drinkin’ Woman. He would then express his gratitude to audiences with the words “glad y’all appreciate classical singing”.

Donaldson had his biggest hit with the soul-jazz anthem Alligator Boogaloo in 1967. He probably stopped changing as a creative jazz artist around this time, but it never mattered that he stayed the same. His show had a rootsy bonhomie that kept it engagingly and unerringly on the road.

He came to favour summaries of the catchy, stripped-down riffs of his hit tunes, and occasional bursts of the sharp-toned double-time bop runs that showed how seriously he understood the idiom, despite his frequently light-hearted presentation of it.

But Donaldson loved his work, and his rheumy, seen-it-all physiognomy registered satisfaction with a young audience’s affection for him. He would sing as much as he played, and slyly milk reactions by delaying the payoffs in the inevitable cadences of the blues, keeping the final chords churning on like a stuck disc.

Donaldson was one of Charlie Parker’s most distinctive alto saxophone disciples when he first surfaced in the 1950s. The secret of Parker’s pervasive influence was his affinity with the blues – a common root that made the music accessible to a non-specialist public, despite the complexity of bop syntax compared to the more lyrical and dance-based jazz that had preceded it.

Parker’s inspirations were adopted and adapted in many ways, but the post-Parker alto saxophonists Cannonball Adderley and Donaldson rarely departed from the blues. Their work did much to inspire the 60s soul-jazz movement – bebop with a preacher’s emphatic cry – and a jazz development that was critical to the evolution of late 20th-century fusion and jazz-funk.

Donaldson, born two years earlier than Adderley – and an influence on the younger man’s development – had an American southerner’s sensitivities to the raw and vocal sound of early blues.

Born in Badin, North Carolina, the second of four children of Louis, a minister, and Lucy, a music teacher and pianist, Lou studied the clarinet as a teenager – all his siblings were musicians – and played in a marching band while studying at North Carolina A&T College, in Greensboro. In 1945 he was drafted into the US navy, where he took up the alto saxophone and joined a navy band that also featured the celebrated swing altoist Willie Smith.

Smith, also Carolina-born, was a significant early influence on Donaldson, with his fluency of ideas and professionalism. Like many Parker disciples, Donaldson then made the move from the south to bebop’s birthplace in New York after the second world war. But he heard the bluesily expressive depths in the new idiom better than many of Parker’s young imitators – his tone was incisive and fierce, his phrasing as emphatic and dramatic as a sermon, while he also had a sophisticated grasp of the method’s harmonic complexities.

The late 1940s also saw some creative meetings between swing jazz and urban rhythm and blues, in the “jump music” style of Louis Jordan, one of the precursors of rock’n’roll. Saxophone players within that full-on idiom had much in common with the young Donaldson’s evolving style.

In 1952 Donaldson made his recording debut with the bop vibraphonist Milt Jackson (a founding member of the Modern Jazz Quartet) and also recorded with the pianist Thelonious Monk. He began working with the powerful young Dizzy Gillespie trumpet disciples Blue Mitchell and Clifford Brown, the pianist and jazz-funk godfather Horace Silver and the drummers Art Blakey and Philly Joe Jones.

All these players were taking the first steps in the development of the gospelly “hard bop” style, a pungent antidote to the vaporous, more intellectualised chamber-jazz manner of the 50s “cool school”. Donaldson also worked briefly with Charles Mingus and the saxophonist Sonny Stitt, but it was his performance with Brown, Silver, Blakey and the Parker bassist Tommy Potter – an encounter documented on the two-volume A Night at Birdland – that led to the founding of one of the most famous bands in the hard bop style, Blakey’s long-running Jazz Messengers.

The Blue Note label was closely associated with the promoting of hard bop, and Donaldson became a regular in the company’s studios. The drive of the Latin-jazz percussionist Ray Barretto was a key element in the jukebox success of the saxophonist’s 1958 album Blues Walk, and John Patton’s holy-rolling Hammond organ stoked up the sermonising atmosphere alongside the infectiously funky guitarist Grant Green on the 1963 Donaldson disc Good Gracious!

The album spawned two hit singles, which found their way on to R&B radio stations that rarely aired jazz.

After working with Blue Note luminaries including Donald Byrd and Wayne Shorter, Donaldson quit the label in search of more funk-oriented marketing in the mid-60s, but returned in 1967 to make the repetitive but popular Alligator Boogaloo – with the organist Lonnie Smith and a young rising star, George Benson, on guitar.

Jazz was then under pressure from a more adventurous and improvisatory rock music, and the pragmatic Donaldson was looking for loopholes, experimenting for a while with the electronic Varitone saxophone. Mr Shing-A-Ling was a subsequent hit, after which Donaldson rarely altered his predominantly funky repertoire in the studios. Titles such as Say It Loud (1968), Hot Dog (1969) and Everything I Play Is Funky (1970) make Donaldson’s target audience clear.

By the later 70s the formula was wearing thin, and for much of the decade Donaldson was in retreat. But the burgeoning club scene of the next decade, with its fervent jazz nostalgia leading to the acid-jazz movement, brought him back for a new dance audience.

In his late 50s, he began recording again – for the Muse, Timeless and Milestone labels – and for the latter company he recorded the album Caracas in the early 90s, with Lonnie Smith back on the Hammond organ stool.

The knowing old veteran still sounded in fine fettle on some favourite themes on the 2000 album Relaxing at Sea: Live on the QE2, with the young trumpeter Nicholas Payton reminding him of the bebop audacity that had first lit his musical flame over half a century before.

His infectious playing was often sampled in later years, and he was made a National Endowment for the Arts Jazz Master in 2012 – a year in which he also made an engaging appearance at Ronnie Scott’s Club in London, affectionately unfurling his old hits like Blues Walk and Alligator Boogaloo. Donaldson retired from live performances in 2017, but regularly attended tributes to him at Dizzy’s Club in Manhattan until his 97th birthday.

He was married for 56 years to his wife, Maker, who died in 2006. He is survived by their daughters, Lydia and Carol.

• Lou Donaldson, saxophonist, born 1 November 1926; died 9 November 2024

• This article was amended on 12 November 2024. Lou Donaldson’s collaborator on the albums Alligator Boogaloo and Caracas was the organist Lonnie Smith, not the keyboardist Lonnie Liston Smith, as the original stated.