In 1941, he volunteered for military duty, serving in the U.S. Army for four years, including two years in the European Theater. From 1946 to 1977, Evins represented Tennessee's fourth congressional district in the U.S. House of Representatives. At the time of his retirement, he was the longest serving member of the House of Representatives in the history of Tennessee and was referred to as the "Dean" of the Tennessee delegation by fellow house members.
Evins served under six U.S. presidents – from Truman to Ford – and chaired the Appropriations Subcommittee on Independent Agencies, which funds boards, bureaus, commissions, agencies and departments of the federal government. He also chaired the Appropriations Subcommittee on Public Works, which funds national public works programs.
He was an early and strong supporter of the space program and obtained support for Arnold Engineering Center, the University of Tennessee Space Institute and Oak Ridge National Laboratory. Congressman Evins was a strong backer of President Lyndon Johnson, and though unpopular at the time, voted for the 1964 Civil Rights Act, a major milestone in United States history.
Evins was also instrumental in the passage of the Model Cities Act, providing funds for cities to build new infrastructure, and succeeded in designating Smithville a Model City, the results of which are evident in its modern infrastructure - one that Evins Mill benefits from to this day.