In 1979 Arinbasarova was named Honored Artist of the RSFSR and in the same year she received the USSR State Prize for her role in The Taste of Bread (1978).

After watching a film in which an excerpt from the ballet "Swan Lake" was shown in her childhood, Natalya desired to become a professional ballerina.

For her performance as Altynai, a peasant girl who supports the Communist teacher in her village, Arinbasarova won the prize for Best Female Lead at the Venice Film Festival in 1966.

Arinbasarova was cast by Tolomush Okeev in the social drama The Ulan (1977), by Polish filmmaker Jerzy Hoffman in Beautiful Stranger (1992), and by Ermek Shinarbaev in the Kazakh-French co-production A Tender Heart (1994).

She also had a supporting role in the Kazakh picture Leila’s Prayer (2002), about a young girl living near the Semipalatinsk nuclear testing site.