A native from Stanley, North Carolina, Abernathy joined the majors after graduating from high school. He changed his pitching motion after shoulder surgery left his career in doubt, switching from a three-quarter delivery and becoming an effective sidearmer who developed a nasty submarine pitch that was almost unhittable.
Abernathy appeared in 681 games and picked up 148 saves during a 14-season career between and , playing for the Washington Senators (1955-57, 1960), Cleveland Indians (1963-64), Chicago Cubs (1966, 1969-70), Atlanta Braves (1966), Cincinnati Reds (1967-68), St. Louis Cardinals (1970) and Kansas City Royals (1970-72). He compiled a 63-69 record with 765 strikeouts and a 3.46 ERA in 1147.2 innings.
In , Abernathy recorded a league-leading 31 saves with the Cubs, along with 104 strikeouts and a 2.57 ERA. He had 28 saves, 88 strikeouts, and a 1.27 ERA two seasons later with Cincinnati. In , Abernathy won 10 games and got 13 saves, and had 10 and 14 in .
Ted Abernathy died in Gastonia, North Carolina at the age of 71.