The latter won bronze in the 55kg weight section. And the triumphs made them the country's only siblings to win World Championship (seniors) medals in an Olympic discipline.
Geeta outclassed Ukraine's Nataliya Synyshyn 3-0 in the final of the repechage round. Maria Prevolaraki of Greece won the other bronze, defeating Canadian Brittaneee Morgana Laverdure.
London Olympic champion Saori Yoshida of Japan, who was also the defending champion, retained her title. The silver went to Helen Louise Maroulis of USA.
Earlier, Geeta lost to Saori in the quarterfinals and got another chance in the repechage round, where she defeated Akziya Dautbayeva of Kazakhstan before winning the bronze playoff bout.
"In the London Olympics, I failed to make a mark. But competing in the Games gave me a lot of exposure and I am happy that I was able to use it in the World Championship," an elated Geeta told HT.
Geeta, who was conferred the Arjuna Award last month, created history by becoming the first Indian woman grappler to compete in the Olympics. "I could have performed better in London but lack of experience cost me dear. After coming back from the Olympics, I started training for the World Championship. The bronze medal will be a stepping stone towards achieving my aim of winning an Olympic medal. For sure, I will make up for the loss at the London Games in Rio (2016)," said Geeta, who won gold at the 2010 Commonwealth Games.