Playing White, Mchediishvili opted for the Open Catalan system against the his lower-ranked Indian rival and soon obtained an advantage from the early middle-game.
However, he could not find the accurate continuation, which allowed Sangma to create counter-play and in the resultant time-scramble, Mchediishvili blundered his 33rd move and soon resigned when in a hopeless position.
Mchediishvili's surprise defeat follows on the heels of Tajikistan GM Amonatov Farrukh's loss in round one yesterday to host country's little fancied Matta Vinay Kumar.
Playing White, Shivananda surprised his rival with a rarely played Bird's Opening. However, Merab was able to equalise easily in the middle game.
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After exchange of most of the pieces, Shivananda was able to win a pawn on move 45 before a gritty rearguard action by the Georgian GM forced him to call truce after 55 moves.
In another upset, one of India's rising stars, GM Sahaj Grover, was beaten by untitled Saravana Krishnan while GM Vokarev Sergey of Russia was held to a draw by A Karthik.