Erzsébet Németh was already involved in athletics in her elementary school years, before playing handball more seriously at the age of 14, in 1967, at the MEDOSZ SE in Csorna. After completing her high school diploma, Németh moved to Budapest in 1972 and became a player for Ferencváros, which had won the championship the previous season, where she spent almost her entire career. Between 1972 and 1980, she won five silver medals and four bronze medals with her team in the first division. The team also achieved great success on the international stage, winning the European Cup Winners’ Cup in 1978, and then reaching the final again in 1979, although they failed to defend their title.
During the successful club years, from 1973, Németh was a member of the national team, which won bronze medals at the 1975 and 1978 World Championships, and the 1976 Olympics, along with a fourth place at the 1980 Olympics in Moskva. Her last significant international achievement, a silver medal, was achieved at the 1982 World Championships in Budapest. In 1986 Németh joined Tatabányai Bányász, where she played for two seasons, and then played for another year in Jászberény. After finishing her active career, she became a coach, first working with the youth and then with adult teams in Csömör and Maglód.