While Sakshi lost 2-9 to Russia's Valeria Koblova in 58kg Freestyle category, it was heartbreak for Vinesh, who was forced to concede her 48kg bout against China's Yanan Sun 1-2 after a freak knee injury.
Sakshi, who trailed 0-1 after the first period, made a comeback in the initial minutes of the second period to go 2-1 up at the Carioca Arena.
She, however, failed to maintain the lead as the Russian overpowered her with some incredible moves to take an unassailable 9-2 lead in the dying minutes.
Sakshi is still in contention for bronze via Repechage if Valeria makes it to the final.
Earlier, Sakshi defeated Moldova's Mariana Esanu Cherdivara on a four point take down criteria to enter the 1/4 final round.
Meanwhile, in the 48kg category, Vinesh's surge was cut short after her Chinese opponent hit back with a single-leg takedown hurting the Indian in the process.
The 21-year-old Haryana grappler was leading 1-0 before hurting her knee as the Chinese gained two points to be declared victorious by injury at the Carioca Arena.
Vinesh, who got her injured knee wrapped, was taken off on a stretcher as the injury seemed to be a very serious one.
Earlier, she got her Rio campaign off to a rousing start by overpowering Romania's Emilia Alina Vuc 11-0 in the 1/8 round after getting a bye in her opening round.
