Morello died Saturday at Trinitas Regional Medical Center in Elizabeth, N.J., said his wife, Jean. No cause was given.
The quartet, with Brubeck on piano, Paul Desmond on alto saxophone, Eugene Wright on bass and Morello on drums, became successful beginning in the late 1950s exploring unusual time signatures. The album "Time Out," which included "Take Five" with Morello's memorable solo and "Blue Rondo á la Turk," became one of the most popular jazz albums ever.
"Drummers worldwide remember Joe as one of the greatest drummers we have known. He was a good friend," Brubeck said in a statement Sunday. "Many people consider the rhythm section of Eugene Wright and Joe Morello in my quartet as being one of the most consistent, swinging rhythm sections in jazz.... His drum solo on 'Take Five' is still being heard around the world."
Morello told Canada's Kingston Whig-Standard newspaper in 2007: "Someone said that drum solo changed the way people drummed because it was more of an abstract solo. We'd use that to close the concert and always get a standing ovation."
Morello was born July 17, 1928, in Springfield, Mass. His vision impaired since birth, he studied the violin before switching to drums in high school. He moved to New York in the early 1950s and worked briefly with Stan Kenton, among others, before becoming a member of pianist Marian McPartland's trio.
Morello joined Brubeck's quartet in the mid-1950s, turning down offers from the Benny Goodman and Tommy Dorsey bands.
"Joe was a drummer's drummer. You could talk to almost any drummer and he'd probably be on their list of the drummers they admire most," jazz critic Don Heckman said Sunday. "He played with such sensitivity and accuracy, and he was always a support for what was happening while keeping the rhythm alive."
Heckman called Morello's "Take Five" solo "pretty extraordinary" for its sense of momentum and emotional intensity. Desmond wrote "Take Five" in a then-unusual 5/4 rhythmic meter.
Ed Shaughnessy, a longtime friend who played drums in the "Tonight Show" band for 29 years, told The Times on Sunday that Morello "developed a style of his own and never played in anything but good taste. He was an ardent practicer. And he got great results."
After Brubeck disbanded the group in 1967, Morello continued to play but primarily was a teacher. His students over the years included Max Weinberg, who gained fame playing with Bruce Springsteen and leading talk-show host Conan O'Brien's band.
Weinberg, in an interview with The Times on Sunday, said he started studying with Morello in the late 1970s. "I sought Joe out. He was a drum guru," Weinberg said. "He took me from a very talented amateur to a pro who could field any kind of musical question asked of me."
Morello appeared on more than 120 recordings, according to a biography on his website.
"For us, the guys in the original classic quartet were like our uncles," one of Brubeck's sons, composer and musician Chris Brubeck, told The Times on Sunday. "Joe was able to master all the odd-time signatures that Dave wanted to explore. Just an amazing player."
Morello's wife was his only immediate survivor.