The 22-year-old Egorian beat Vilikaya in the final match 15:14. The bronze medal went to Ukrainian Olga Kharlan, who overcame French fencer Manon Brunet by the score of 15:10.
The Rio gold medal was the first to be won by a Russian female athlete in the individual saber Olympic event since 1968.
Before winning the Olympic gold, Egorian won one gold medal at the World Championship and four gold medals at the European Championships.
Velikaya has now become a two-time Olympic silver medal winner, in addition to her seven World Championship gold medals and 11 gold medals from European Championships.
Team Russia now has 2 gold, 3 silver and 3 bronze medals.