Career
He served as the head football coach at the University of Missouri from 1971 to 1977, compiling a record of 38–41. He spent 13 years, from 1958 to 1970, as an assistant coach at Missouri under Dan Devine. His Missouri football teams upset the Notre Dame Fighting Irish on October 21, 1972 at South Bend, Indiana, the Alabama Crimson Tide on September 8, 1975, at Birmingham, the USC Trojans at Los Angeles on September 11, 1976, the Ohio State Buckeyes at Columbus two weeks later, and the Arizona State Sun Devils at Tempe on October 1, 1977, during his final season at Missouri.
In his seven years at Mizzou, Onofrio compiled a 1–6 record against arch-rival Kansas, which contributed to his dismissal. Onofrio coached four All-Americans and 30 future National Football League players. Onofrio was a 1993 inductee to the Missouri Intercollegiate Athletic Hall of Fame.
He died on November 5, 2004 in Tempe, Arizona.