Enrico Fazio was born in Turin on 2 January 1956. He began on guitar, studying privately with the same jazz guitarist as Claudio Lodati, taught himself electric bass in blues groups, and then studied double bass at the Alessandria Conservatory and music analysis at university. His own biography lists a master's degree in double bass and a bachelor's degree with honours in music disciplines. In the European Year of Music, 1985, he won a scholarship from the Cini Foundation in Venice, and in 1989 he took first prize in the National Competition of Jazz Composition and Arrangement at the Sant'Anna Arresi festival, a prize dedicated to Charles Mingus.

He began playing professionally in 1974 as a co-founder of Art Studio, the Turin quartet formed with Lodati, saxophonist Carlo Actis Dato and drummer Fiorenzo Sordini. Their debut LP appeared on Drums Edizioni Musicali in 1977 and four more followed on CMC between 1978 and 1986. Three years after Art Studio's founding, in 1977, Fazio was among the musicians who founded Centro Musica Creativa, one of the first self-managed cooperatives for contemporary jazz and research music in Italy. He served as its president from 1992 to 2000. Twelve of the credits on his Discogs page carry a CMC label imprint.

From 1983 to 2006, by his own account, he was the bassist in Actis Dato's quartet. The Discogs record shows him on Noblesse Oblige (recorded 1986) through Swingin' Hanoi (recorded 2003) with saxophonist Piero Ponzo and Sordini, a lineup that made eleven records without a personnel change, according to Actis Dato's profile on this site. Art Studio kept going as well, with the 1994 compilation The Complete C.M.C. Sessions, the 1997 album Off Limits, the thirtieth-anniversary concert record Trenta_Live in Torino (recorded 2004, released 2007) and Rendez Vous (2013), on which saxophonist Francesco Aroni Vigone and pianist and singer Irene Robbins complete the lineup.

Since 1987 he has also led his own groups. Mirabilia! (CMC, 1988), billed as the Enrico Fazio Quintet, credits eight players, among them Alberto Mandarini on trumpet, Actis Dato, Sordini and Aroni Vigone. Lieto Fine (1989) was recorded by a 17-piece ensemble, Euphoria (Splasc(h), 1991) by the quintet again, and Gracias! (1995) by a 6tet and 10tet that combined a 1995 studio session in Mondovi with a 1991 live set from Buenos Aires. In 2003 the septet, now on Leo Records, released Zapping!, which Fazio describes as a recycling project: hundreds of excerpts from baroque, jazz, rock, Balkan, opera and film music reused out of context inside his own writing. Its front line paired Mandarini with Fabrizio Bosso, and his site lists it fourth in the Top Jazz 2003 record-of-the-year poll. Live In Milano: Villa Litta (2005) followed, recorded on 27 August 2004 with Emanuele Parrini on violin.

The most recent phase runs through Critical Mass. Shibui (Leo, 2013) and Wabi Sabi (Leo, 2019) feature Mandarini, Aroni Vigone, reed players Gianni Virone and Adalberto Ferrari, trombonist Gianpiero Malfatto, violinist Luca Campioni, and on Wabi Sabi violinist and mandolin player Anaïs Drago, theremin player Valeria Sturba and kora player Moustapha Dembele. The Musica Jazz review of Wabi Sabi, in November 2019, called it one of the records of the year, and the We Insist! Foundation's artist page reports a second-place finish in Top Jazz 2019. Girotondo (We Insist! Records, June 2022) is a twelve-track ensemble record recorded on 26 April and 3 May 2014 at (52+1) Studio in Agliano Terme. It takes its structure from Arthur Schnitzler's play La Ronde: musicians are matched at random to the play's characters and play in pairs, each pair overlapping the next, with Fazio adding electronic introductions as an outside narrator. Alongside it came 7 Rocks (In Viaggio), seven duets with clarinetist Giancarlo Locatelli, recorded in a single 2014 session and released on We Insist! in December 2022.

Outside his own name Fazio has recorded with a wide circle of European improvisers. He plays on the Anglo Italian Quartet's Put It Right Mr. Smoothie and Twice Upon a Time, with British saxophonist Elton Dean and trumpeter Harry Beckett; on Locatelli's quintet album Trochus (1991), on which Steve Lacy plays soprano saxophone on three tracks; on the Vapirov Project's Waltz Str. (1994), recorded at the Varna Summer festival in Bulgaria, alongside Pino Minafra and Actis Dato; and on L'Invenzione Del Verso Sfuso (1989), a live Noci festival project of Minafra, Actis Dato and the poet Vittorino Curci. He recorded Senza Parole (1990) and A Piece Of The Rock (1992) with American singer Ellen Christi, and Onde (1987) with Art Studio and singer Tiziana Ghiglioni. His own biography also names Keith Tippett, Gianluigi Trovesi, Massimo Urbani, Claudio Fasoli and Daniele Cavallanti among his collaborators; none of them appears in his Discogs credits, so these are reported as his own account rather than as confirmed sessions.

Fazio teaches at the "A. Vivaldi" Conservatory in Alessandria, where he is Professor of Jazz Composition and Arranging and head of the jazz department. Italian Wikipedia dates his teaching career to 1987, his own site to 1999. Drago completed a jazz composition degree under him in 2017. His site says he has suspended concert activity in recent years to concentrate on composition, teaching and record production, mainly with Critical Mass.

Fazio writes for medium-large ensembles and treats composition and improvisation as a balance to be tuned record by record. Zapping! is the clearest statement of the method: existing music is quoted, reshuffled and reset inside a fixed compositional identity. The Penguin Guide to Jazz, as cited on Italian Wikipedia, heard carnival colours and offbeat energy in the band, and Musica Jazz's reviewer of Wabi Sabi heard a melodic emphasis reminiscent of Charles Mingus. Wabi Sabi takes its title from the Zen idea of beauty in imperfection, and Fazio recorded it without preparatory rehearsals, following Steve Lacy's line about being ready to make mistakes. Girotondo shows the other side of the same approach: a rigorous plan (a chain of paired dialogues, twelve-tone series, the ensemble as a ring) that leaves the actual playing to the musicians. On his own records he doubles on balafon (Zapping!, Shibui), stick bass (Gracias!) and electronics (Wabi Sabi, Girotondo), and his bass work in Art Studio and Actis Dato's quartet came out of the Turin cooperative scene he helped build.