Eduardo Palmieri was born in New York City on December 15, 1936, the second son of Isabel Maldonado and Carlos Manuel Palmieri, who had come north from Ponce, Puerto Rico and settled in the South Bronx in 1925 and 1926. His older brother by nine years, Charlie, was already a piano prodigy, and the two of them worked the talent-contest circuit together while Eddie was still a boy. He took lessons, played Carnegie Hall at eleven, and at thirteen joined an uncle's orchestra as a timbalero rather than a pianist, a detour that left a permanent mark on how he attacked a keyboard. He formed his first band at fourteen. Through the 1950s he worked as a sideman in the New York Latin dance orchestras, including Eddie Forrester's group, Johnny Segui's band and, most importantly, the orchestra of Tito Rodríguez.

In 1961 he left Rodríguez and started Conjunto La Perfecta with the singer Ismael Quintana. The pachanga craze was at its height and the standard vehicle was the charanga, a violins-and-flute ensemble, so Palmieri did the obvious thing backwards: he threw out the violins and put in two trombones. Charlie named the hybrid the "trombanga" in the liner notes of the first album, and the sound it produced, hard, low and blaring, was copied across New York within a few years, most conspicuously by Willie Colón. The founding band was Barry Rogers on trombone, George Castro on flute, Manny Oquendo on bongos and timbales, Tommy López on congas and Dave Pérez on bass. It was Rogers who, around 1964, put John Coltrane and McCoy Tyner records in front of Palmieri. Tyner became the reference point he named for the rest of his life, and the quartal voicings and the churning left hand that mark his playing from that moment forward come directly out of those records.

Two things happened in the middle of the decade that pulled the jazz half of his work into the open. On Mambo Con Conga Is Mozambique (Tico, 1966) he brought over the mozambique, a rhythm developed in Cuba after the revolution, and built a dance record on top of it that swung in a way Latin dance records generally did not. And in the same year he made El Sonido Nuevo with the vibraphonist Cal Tjader for Verve, his first record for a jazz label, with Julian Priester and Mark Weinstein in the trombone section, arrangements split between Palmieri and Claus Ogerman, and the lacquer cut by Rudy Van Gelder. A second Tjader album, Bamboleate, followed in 1967. Alongside this he was reading the Schillinger system, introduced to him by the singer Bob Bianco, which gave him a formal vocabulary for the harmonic experiments he was already making by ear.

The band broke up in 1968 over money, and what he built in its place was harder and stranger. Justice / Justicia (1969) put his politics on the sleeve. Superimposition (1970), made with Alfredo "Chocolate" Armenteros on trumpet, Andy Gonzalez on bass and Nicky Marrero on timbales, splits itself down the middle: a side of vocal dance numbers and a side of instrumentals, of which "17.1" and "Chocolate Ice Cream" are the two pieces jazz musicians still take off the record. Harlem River Drive (Roulette, 1971), billed to the band rather than to him, put salsa, soul, funk and jazz through the same arrangement and refused to separate them again. Vamonos Pa'l Monte, from the same year, had Charlie at the organ and Palmieri at a Fender Rhodes, the first salsa pianist to record on one. In 1972 he took a band into Sing Sing prison and recorded there. On July 21, 1979 he played the Amandla Festival in Boston alongside Bob Marley, Dick Gregory and Patti LaBelle.

The Coco Records years brought the first of the awards. The Sun Of Latin Music (1974), arranged by René Hernández with the eighteen-year-old Lalo Rodríguez singing, won the very first Grammy given in the newly created Best Latin Recording category, at the 18th Grammy Awards. Its centrepiece, "Un Día Bonito", opens with several minutes of unaccompanied free piano before the band arrives, which was not what the salsa market of 1974 expected from a hit record. Unfinished Masterpiece followed in 1975, released by the label over his objections while he still considered it incomplete, and won anyway. In 1978 Epic gave him a major-label budget and he spent it on Lucumi, Macumba, Voodoo, a record of Afro-Caribbean ritual rhythm under written string and horn parts. Three more Grammys came in the 1980s, all of them in the tropical dance category rather than a jazz one: Palo Pa' Rumba (1985), Solito (1986) and La Verdad (1988), the last made with the singer Tony Vega. Charlie died suddenly in 1988. In 1989 he made Sueño for the German jazz label Intuition, with David Sanborn on alto and Brian Lynch and Charlie Sepúlveda on trumpets.

From the mid-1990s the jazz work stopped being an occasional excursion and became a parallel career with its own working band. Palmas (Elektra Nonesuch, 1994) was the first, an instrumental quintet-plus record with Brian Lynch, Conrad Herwig and Donald Harrison in the front line, and it drew a nomination for Best Latin Jazz Performance in the category's first year. Arete (1995), Vortex (1996) and El Rumbero Del Piano (1998) continued it, Harrison's alto among the horns throughout. In 1998 the Berklee College of Music gave him an honorary doctorate. He announced his retirement in 2000 and then immediately recorded Masterpiece / Obra Maestra with Tito Puente, taped shortly before Puente's death and released in the year he died; it took two Grammys. In 2002 he revived the trombone front line as La Perfecta II for Concord Picante, and in 2005 Listen Here!, with Herwig, Lynch, Harrison, Giovanni Hidalgo and Horacio "El Negro" Hernandez, won Best Latin Jazz Album at the 48th Grammy Awards. The following year Simpático, co-billed to Brian Lynch, won it again at the 49th, on a session that ran Phil Woods, Yosvany Terry, Pedrito Martinez, Little Johnny Rivero, Dafnis Prieto and Lila Downs through his band.

In 2013 the National Endowment for the Arts named him an NEA Jazz Master, the highest honour the United States confers in jazz, in a class with Mose Allison, Lou Donaldson and Lorraine Gordon. He was eighty when he made Sabiduría (Ropeadope, 2017), his first leader album in eleven years, and eighty-one when he released two more in 2018: Full Circle, a set of re-recordings of his own early repertoire with the current band, and Mi Luz Mayor, a record of boleros and danzones dedicated to his wife Iraida, who had died in 2014, with Carlos Santana playing guitar on it. He kept working almost to the end: fronting the young band Sonido Solar in 2022, appearing in Spike Lee's Highest 2 Lowest in 2025, and playing on Conrad Herwig's Reflections: Facing South, issued the same year. He passed away at his home in Hackensack, New Jersey on August 6, 2025, at eighty-eight.

Palmieri played the piano like a percussionist who had been given a harmony textbook, which is close to what he was: he came up on timbales, and the dissonant, hammered, rhythmically displaced block chords he used to drive a band forward have more in common with a tumbao played on drums than with anything in the salsa piano tradition he grew out of. The named influences are Thelonious Monk and McCoy Tyner, with his brother Charlie ahead of both, and the debt to Tyner is specific and audible: quartal voicings, a heavy left hand, and a habit of letting harmony pile up until it strains. What he did with it was uncommon. Rather than laying jazz solos over a Latin rhythm section, he built pieces on the Cuban descarga, the open jam, and then "opened up" the arrangements so his sidemen soloed as jazz musicians inside a dance structure, which is why Superimposition can carry a vocal side and an instrumental side without sounding like two records. The Schillinger system gave the harmonic reaching a method, and by the 1970s he was writing free piano introductions into commercial salsa records and expecting the audience to follow. He never used the word salsa for his own music, holding with Tito Puente that it was a marketing term invented to sell New York Latin music rather than a description of anything. AllMusic files him under both Latin and jazz and lists Afro-Cuban Jazz, Cuban Jazz, Global Jazz and Latin Jazz ahead of New York Salsa among his styles, which is a fair summary of a career that ran the two side by side for sixty years.