He began performing at 13 and recorded with his jazz trio at 16. In the 1950s and 1960s Gaslini performed with his own quartet. He was the first Italian musician mentioned as a "new talent" in the Down Beat poll and the first Italian officially invited to a jazz festival in the USA (New Orleans 1976-77). He collaborated with leading American soloists, such as Anthony Braxton, Steve Lacy, Don Cherry, Roswell Rudd, Eddie Gomez, Max Roach, Nacci Alberto, but also with the Argentinian Gato Barbieri and Frenchman Jean-Luc Ponty. He has also adapted the compositions of Albert Ayler and Sun Ra for solo piano, which the Soul Note label has issued. He also composed the soundtrack of Michelangelo Antonioni's La notte (The Night, 1961).
From 1991 to 1995 Gaslini composed works for Carlo Actis Dato renowned Italian Instabile Orchestra. As to contemporary music, he composed symphonic works, operas and ballets represented at the Scala Theatre in Milan and other Italian theatres, in addition to music for the stage and about 20 film scores. He has been deemed a godfather of hardcore improvised music in Italy and has been the first holder of jazz courses at the Santa Cecilia Academy of Music in Rome (1972–73).