Evensville is an unincorporated community in Rhea County, Tennessee, United States. Evensville is located along U.S. Route 27 5.8 miles northeast of Dayton. Evensville has a post office with ZIP code 37332. Rhea County High School is located in Evensville.The community is believed to have been named for an early settler, Andrew Evens, or one of his relatives.Rhea County Schools operates public schools. Rhea County Middle School and Rhea County High School are in Evensville.