Courtesy Nair's 134 off 229 balls with 17 boundaries, Karnataka scored 332 in their second innings ending with an overall lead of 379 runs.
At stumps, Hyderabad were 92 for 2 with Tanmay Agarwal batting on 43. They need another 288 runs on the final day while Karnataka need to take eight wickets.
The day belonged to Nair, who scored his 11th first-class hundred. The century came after a prolonged bad patch that saw him getting dropped from the Indian team and also have modest returns during India A tours.
Along with India discard Stuart Binny (72), who got his second half-century of the match, he added 160 runs for the fifth wicket. Binny's runs came off 144 balls with eight boundaries and a six.
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Left-arm spinner Mehdi Hassan was the main wicket-taker for Hyderabad with figures of 5 for 88.
With track offering significant help to the spinners, off-spinner Krishnappa Gowtham and leg-spinner Shreyas Gopal are expected to do bulk of the bowling on the final day.
Group A
In Shimoga
Karnataka 183 and 332 (Karun Nair 134, Stuart Binny 72, Mehdi Hassan 5/88); Hyderabad 136 and (target 380) 92/2 (Tanmay Agarwal 43 batting)
In Guwahati:
Assam 244 & 41/7 (Kunal Saikia 16, Anureet Singh 3/18); Railways 483/7 (Arindam Ghosh 109, Nitin Bhille 89, Shivakant Shukla 86)
In Lucknow:
Maharashtra 312 and 256/4 (Rahul Tripathi 91, Ankit Bawne 58). Uttar Pradesh 271 (Almas Shaukat 63, Suresh Raina 0, Chirag Khurana 6/53).
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