The 23-year-old from Haryana, a silver medallist at the 2014 Glasgow Commonwealth Games and bronze winner at the 2014 Incheon Asian Games, earned a dramatic come-from-behind win over Kyrgysztan's Aisuluu Tynybekova to script history.
Weight-lifter Karnam Malleshwari was the first Indian to win an Olympic medal for India when she won a bronze at the 2000 Sydney Games.
Overall, Sakshi has won India's fifth wrestling medal in the Olympic Games.
KD Jadhav was the first wrestler from India to win a medal in Olympics with his bronze at the 1952 Helsinki Games.
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Sushil Kumar, who missed out of the Rio Games after a controversy, bagged the second wrestling bronze medal at the 2008 Beijing Games before clinching a silver at the London Games where Yogeshwar Dutt also pocketed a bronze.
The inspiring show by Sakshi lifted the gloom that had descended over the Indian contingent that spent 11 days waiting for a medal.
It is India's 25th medal in Olympic Games.