Middle order batsman Khanolkar made a sedate 81 from 205 balls to lift his side to 323 on the second day at the Karnail Singh stadium.
Khanolkar shared a 106-run stand with G Shankar Rao who made a relatively quick 40 with four fours and a six.
In reply, Karnataka were 134 for three at stumps.
Captain Sujit Somasundar hit a patient 46 before being bowled by a low kept delivery from part-time left arm spinner Tejinder Pal Singh as close approached.
However, Sudhindra Shinde, with whom Somasundar added 70 runs for the third wicket, remained at the crease after a watchful 49 not out.
Stuart Binny, son of former Test all-rounder Roger Binny, was at the other end on a dad-like 19 from 24 balls with four fours.
Karnataka were still 189 runs behind in the first innings.
"The wicket had settle down after the first day. It is good for batting," Somasundar said on his bowlers' inability to break the crucial Khanolkar-Rao association that threw a lifeline to who were sinking at 186 for five on the first day.
Vinay Kumar, who did the damage yesterday, picked both the wickets of Khanolkar and Rao to claim his first five-wicket haul of 5-65.