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.

In 1957, Rubtsova took part in the inaugural Women's Chess Olympiad in Emmen, the Netherlands, as a member of the USSR team, along with Kira Zvorykina.

She finished second in the next championship, only losing the title to Lora Yakovleva on tie-break, and fifth in the one after that.

As of today, she remains the only player, male or female, to become world champion in both over-the-board and correspondence chess.