[2] Fannin and his family moved to Phoenix, Arizona, when he was eight months old due to his father's health.

[6] A conservative Republican,[7] Fannin was elected Governor of Arizona in 1958, defeating Attorney General Robert Morrison by nearly 30,000 votes.

[5] During his tenure, Fannin increased funding for the public school system by raising sales taxes, equalized property taxes, established the first medical school in the state, and created the Arizona-Mexico Commission to promote tourism and trade across the border.

He defeated Democrat Roy Elson, an aide to Senator Carl Hayden, by a 51–49% margin.

As the ranking Republican on the Senate Interior Committee, he was a spokesman for Presidents Richard Nixon and Gerald Ford on energy policy; he opposed new limits on strip mining and tighter reins on federal lands.

[7] He also joined conservative Democratic Senators to preserve the clause of the Taft–Hartley Act that let the states decide whether to prohibit mandatory membership for workers in unionized shops.