Jacquet died of a heart attack Thursday at his New York City home, said longtime friend and collaborator Dan Frank.
During a career spanning eight decades, Jacquet played with such music greats as Louis Armstrong, Nat King Cole, Dizzy Gillespie, Charlie Parker, Jo Jones, Buddy Rich, Ella Fitzgerald, Miles Davis and Gene Krupa.
When he was 19, he played the tenor saxophone solo on "Flying Home" with Hampton. He likened the performance to a religious experience. "Something was with me at that moment," he said. "It all came together for some reason."
Jacquet, who defined the jazz style called screeching, was known as much for his trademark pork pie hat as the innovative playing style.
He played tenor sax in the Count Basie and Cab Calloway bands and since 1981 performed with his own band, the Illinois Jacquet Big Band.
Jacquet played "C-Jam Blues" with former President Bill Clinton, an amateur saxophonist, on the White House lawn during Clinton's inaugural ball in January 1993. He also performed for Presidents Jimmy Carter and Ronald Reagan.
During his heyday in the 1940s and 1950s, Jacquet recorded more than 300 original compositions, including three of his biggest hits, "Black Velvet," "Robbins' Nest" and "Port of Rico."
Born Jean-Baptiste Jacquet in Broussard, La., his mother was a Sioux Indian and his father, Gilbert Jacquet, a French-Creole railroad worker and part-time musician.
The nickname Illinois came from the Indian word "Illiniwek," which means superior men. He dropped the name Jean-Baptiste when the family moved from Louisiana to Houston because there were so few French-speaking people there.
Jacquet, one of six children, began performing at age 3, tap dancing to the sounds of the Gilbert Jacquet band. He later played the drums in his father's band but discovered his true talent when a music teacher introduced him to the saxophone.
After graduating from high school, Jacquet moved to California where he soon earned a reputation as a little guy who played a lot of sax.
His first exposure was a command performance by Cole, who lined up bass player Jimmy Blanton, Sid Catlett on drums and guitarist Charlie Christian from the Benny Goodman Orchestra and told Jacquet he wanted to hear what he could do.
Years later, Jacquet told an interviewer that playing in that jam session "was like playing with God, St. Peter and Moses," yet he wasn't nervous because "when you play with the greatest you play even better."
Jacquet appeared with Calloway's band in the Lena Horne movie "Stormy Weather" and in the Academy Award-nominated short film "Jammin' the Blues" with Billie Holiday and Lester Young. He replaced Young in the Count Basie Orchestra in 1946 and was given the nickname "The King" by Basie.
During the 1960s and 1970s, he toured extensively in Europe. In 1983, he became the first jazz musician to become artist-in-residence at Harvard University. His stint as guest lecturer at the Ivy League school caused him more angst than any performance of his life, said Carol Sherick, his longtime companion and manager of more than 20 years.
"When he's on stage with a horn in his hand, he's comfortable, but put him in front of a class, just talking ... that's a whole different thing," she said.
Despite his fame, Jacquet lived quietly in New York City's borough of Queens. His wife said he followed Basie to Queens in 1947 but stayed because "the cost of parking his car in Manhattan was more than the rent on his apartment."