[4] On the Republican side, incumbent Senator Edward Gurney chose not to run for re-election after being indicted for allegedly taking bribes in return for his influence with the Federal Housing Administration.

In the general election, Stone narrowly defeated Eckerd in a race that saw the American Party candidate, John Grady, claim nearly 16% of the vote.

During Stone's term in the U.S. Senate, he was a member of the Foreign Relations Committee and was a strong advocate for the Panama Canal Torrijos–Carter Treaties.

[4] He led efforts to secure congressional aid for Israel and also served as an important advisor during the 1978 Camp David Peace Treaty.

[4] Six Democrats entered the race for Stone's seat including his 1974 runoff opponent Bill Gunter who was Florida State Treasurer/Insurance Commissioner in 1980.

[11] From 1981 to 1982, he was senior resident partner at the law firm of Proskauer, Rose, Goetz & Mendelsohn in Washington, D.C.[5] During that time, the Spanish-speaking Stone[12] worked as a paid lobbyist for the right-wing Guatemalan government of Fernando Romeo Lucas García.

[5] In February 1983, Stone served in the Department of State as Special Representative of the President for Public Diplomacy in Central America.

[5] On April 28, 1983, President Reagan announced Stone's appointment as Ambassador at Large and Special Envoy to Central America.

Despite concerns over his recent ties with the oppressive right-wing Guatemalan government and how he would be perceived by the leftist FMLN of El Salvador, Stone was confirmed and commenced the position on May 26.

This made Democrats argue that he was ill-suited to be President Reagan's appointee to be Ambassador at Large for Central America, a role that required negotiation with the leftist government of El Salvador and other administrations.

[17] He resigned effective March 1, 1984, allegedly after experiencing personality conflicts with Assistant Secretary of State for Inter-American Affairs, Langhorne A.