The total gave Karnataka a huge first innings lead of 405 runs before they reduced ROI to 114 for three in their second innings, leaving the visitors trailing by 291 runs with seven wickets in hand.
Karnataka first skittled out the visitors for 201 in their first innings and then batted with responsibility to reach 606 all out with Gautam cracking a sparkling century.
At stumps, Baba Aparajith and Dinesh Karthik were batting on 42 and nine runs respectively for Rest of India.
The India discard edged one to Manish Pandey at second slip, who took a magnificent diving catch.
Opener Jiwanjot Singh (7) also failed to impress dismissed by Vinay Kumar. Kedar Jadhav scored 44 in 65 balls with seven hits to the fence, before he was scalped by spinner Shreyas Gopal.
The 27-year-old Gautam notched up his ninth first-class century while Vinay Kumar (31) and Abhimanyu Mithun (34) chipped in to script useful partnerships with the wicketkeeper-batsman.
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