Kilius, the daughter of a hairdresser, began as a singles skater but picked up pairs very early. Her first partner was Franz Ningel. They placed fourth at the 1956 Olympics and won the silver medal at the 1957 World Championships. Kilius was still a child when she was paired with Ningel, who was more than six years her senior. By 1957 she had grown to be taller than he was, which caused problems on their lifts, so the team split up.
For a time following her split with Ningel, Kilius competed in artistic roller skating as a singles skater. She was the World Roller Lady Champion in 1958.
Meanwhile, in 1957, Kilius began skating with Hans-Jürgen Bäumler under the tutelage of Erich Zeller. Between 1958 and 1964, they won the German Championships four times, European Championships six times and the World Championships two times. Their first World title, in 1963, followed cancellation of the 1961 event due to the crash of Sabena Flight 548 and a collision during their performance at the 1962 World Figure Skating Championships that forced them to withdraw.
Kilius and Baumler also captured the silver medal at the Olympics twice, in 1960 and 1964. In 1966, it was alleged that the team had signed a professional skating contract before the 1964 Winter Olympics – against the rules at the time – and they were stripped of the medal. The IOC dismissed the charges in 1987, reinstated the original results, and Kilius and Baumler were re-awarded their silver medals.
Kilius was voted the German female athlete of the year in 1959. In 1964, she married Werner Zahn, the son of a factory owner from Frankfurt/Main. The couple divorced, and Kilius also divorced her second husband. She has two children, Sascha and Melanie Schäfer, and as of May 2005, two grandchildren.