In May 1942, Tudor passed the theory examination to become an associate of the American Guild of Organists. In the fall of 1943, he assumed the position of organist at Trinity Church in Swarthmore, while also serving as organist at Swarthmore College (1945–47). When he was seventeen, Tudor heard a performance by the Rumanian-born pianist Irma Wolpe (born Schoenberg, later Rademacher) at Swarthmore and was inspired to begin piano studies with her. He quickly mastered the traditional piano literature, then gravitated toward the music of Wolpe's husband, the composer Stefan Wolpe, with whom he prepared such demanding scores as Battle Piece (1943–1947) for performance. Deemed medically unfit for military service in March 1944, Tudor pursued his performing career. He gave solo organ recitals at Trinity Church and, beginning in 1945, duo piano and chamber concerts primarily in New York City, featuring work by Wolpe, Arnold Schoenberg, Stravinsky, and other modernists. He also accompanied the dancers Katherine Litz and Jean Erdman.

The close exchange with Stefan Wolpe set the stage for Tudor's future collaborative work. On December 17, 1950, at Carnegie Recital Hall in New York, he gave the American premiere of Pierre Boulez's Deuxième (1948), a technically demanding work that challenged classical forms and temporal continuity. The success of this performance propelled Tudor into the international spotlight and, the following year, into a position as pianist for a group of four young New York composers: John Cage, Morton Feldman (a former student of Wolpe's), Earle Brown, and Christian Wolff.

This group of experimentalists invented graphic scores for Tudor's realization at the piano, using procedures of chance and indeterminacy. Each new piece challenged his technical command and his practice of transforming the indeterminate graphics and instructions into fully notated performance scores. Tudor held positions as pianist-in-residence and instructor at Black Mountain College in Asheville, North Carolina (summer sessions, 1951–1953) and at the Internationale Ferienkurse für Neue Musik in Darmstadt, Germany (1956, 1958, 1959, 1961), where he introduced works by composers of the American and European avant-gardes, including La Monte Young, Terry Riley, Toshi Ichiyanagi, Sylvano Bussotti, and Karlheinz Stockhausen. He performed piano and electronic music with the Merce Cunningham Dance Company from its inception in the summer of 1953 and, upon Cage's death in 1992, succeeded him as music director of the Cunningham Company.

Tudor's earliest original compositions, like his piano performance, emerged through collaboration. He created Bandoneon! (a combine) for the performance series "Nine evenings: theatre and engineering," held in October 1966 at the 69th Regiment Armory in New York City and organized by Experiments in Art and Technology. Tudor and his fellow participants, among them Cage, Lucinda Childs, Öyvind Fahlström, Yvonne Rainer, Robert Rauschenberg, and Robert Whitman, worked with more than forty engineers and scientists from Bell Telephone Laboratories to develop technical equipment utilized in the performances. The bandoneon produces audio signals programmed to activate television images, lighting, and moving loudspeakers. The subtitle, "a combine," invokes Rauschenberg's three-dimensional assemblages of the 1960s and refers to the composite nature of Tudor's piece.

The interplay of electronic sound, visual imagery, and performance space also guided Tudor's collaboration with sculptors Robert Breer and Forrest Myers and architect Whitman on the Pepsi Pavilion at the Osaka World's Fair in 1970. Commissioned as one of the core artists, Tudor conceived the interior of the pavilion dome as a sound environment and, with the American composer Gordon Mumma, constructed an eight-channel system that sent source sounds in every direction around the listener. His performed installation Rainforest IV grew out of his 1973 New Hampshire workshop that included the musicians John Driscoll, Bill Viola, and Ralph Jones. Tudor's program notes instruct artists to drive source materials through resonant found objects, amplified by means of small microphones (transducers). A pickup system distributes the new resonances through the performance space, and the audience is invited to move freely among the sculptures. In 1973 Tudor formed Composers Inside Electronics, an ensemble dedicated to the composition and performance of live electronic music using circuitry designed and built by the individual composers. Driscoll, Viola, Jones, Paul De Marinis, Linda Fisher, Phil Edelstein, and Martin Kalve were members.

During the 1970s and 1980s, Tudor worked closely with the French artist Jackie Matisse on installations for electronics and kite sculptures, including Sea Tails (1983), Tailing a Dream (1985), 9 Lines, Reflected (1986), and Lines and Reflections (1988). From 1968 until his death, he regularly received commissions from the Merce Cunningham Dance Company. His Soundings: Ocean Diary (1994), together with Andrew Culver orchestral score, constitutes the musical accompaniment to Cage and Cunningham's last collaboration, Ocean, a work for dancers and large orchestral forces positioned around the audience. A film by Molly Davies, David Tudor's Ocean, documents Tudor's final performance with the Cunningham troupe. He died in 1996 at his home in Tomkins Cove, New York.