In reply to Punjab's first innings total of 270, Karnataka ended the third day's play at 351 for five with Nair batting on his career best score of 107 in company of comeback man Amit Verma, who struck an unbeaten 65.
The duo added 110 runs for the unbroken sixth wicket stand as Harbhajan Singh and Co. Were left frustrated with Manish Pandey (65) and wicketkeeper-batsman CM Gautam (48) also making useful contributions.
With first day's play lost due to inclement weather, the match has effectively turned into a four-day affair where Karnataka will be aiming to bat Punjab out of the contest.
22-year-old Nair, who made his first-class debut this season, scored an even-100 against Uttar Pradesh in the Ranji Trophy quarter-final, while he scored his maiden ton (105) against Delhi at the Feroz Shah Kotla in the match prior to that.
He faced 191 balls during the day hitting nine fours. His innings was a mix of caution and aggression. While he punished the loose balls, he did wait for his chance when the Punjab bowlers were doing a good job.
He came in at the fall of Robin Uthappa (47), who was trapped in-front by Harbhajan with an off-break, as Karnataka were at 94 for three.
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