The national team consisting of Angelina Melnikova, Vladislava Urazova, Lilia Akhaimova and Victoria Listunova scored 171.629 points.
American women ranked second (170,562), while Chinese women ranked third (166,863).
The final will take place on July 27.
Earlier, the record holder for the number of performances at the Olympics among gymnasts Oksana Chusovitina from Uzbekistan announced her retirement after her performance in qualifying in the all-around at the Games in Tokyo.