In 1979, Gavitt, along with several other college athletics administrators, helped to form the Big East Conference as a means to better compete with the major schools in the country.

During his tenure, six of the conference's schools (Georgetown, Villanova, Saint John's, Providence, Seton Hall and Syracuse) participated in the Final Four, and all nine teams made it to the NCAA tournament at least once.

His contributions are memorialized in the Dave Gavitt Trophy, given to the winner of the Big East's men's basketball tournament, which he was responsible for not only creating, but its annual use of Madison Square Garden.

In 1980, he was selected as the head coach of the Olympic basketball team, only to lose out on the opportunity due to the boycott of the Moscow games by the United States.

Besides these responsibilities, Gavitt was CEO of the Boston Celtics from 1990 to 1994, President of the NCAA Foundation from 1995 to 1997, and Chairman of the Board of the Naismith Memorial Basketball Hall of Fame until 2003.

He became the third former member of the Friar athletic program (after John Thompson and Lenny Wilkens), and the first native of Rhode Island to be enshrined.