Rubtsova won the Soviet Women's Championship four times (1927, 1931, 1937 and 1948). She was second in the Women's World Chess Championship 1949–50, a point behind Lyudmila Rudenko. She won the title in 1956, finishing ahead of Rudenko and Elisaveta Bykova in a tournament. Rubtsova lost it to Bykova in a match in 1958.