Zutshi won the women's silver medals for the 800 m in 1982, and for the 1500 m in both 1978 and 1982. As the top Indian woman athlete at the 1982 Asian Games in New Delhi, she took the oath on behalf of the competitors during the opening ceremony. For her achievements she has been awarded the Arjuna award and the Padma Shri.
She has inspired other Indian women, such as Bachendri Pal, the first Indian woman to successfully climb Mount Everest. As a child, Pal began to aspire to national fame after seeing a newspaper photograph of Zutshi with Prime Minister Indira Gandhi.
|1978||Asian Games||Bangkok, Thailand||1st||800 m|
|1981||Asian Championships||Tokyo, Japan||1st||800 m|
|1982||Asian Games||New Delhi, India||2nd||800 m|