The Maharashtra batsman rallied Rest of India to 264 from a precarious 102 for five.
There were other handy contributions from Naman Ojha (34), Jayant Yadav (26), Paras Dogra (26) and tail-ender Varun Aaron (25).
The effort was enough for Rest of India to take a 20-run lead over the Ranji Trophy champions, who had succumbed to Aaron's lethal bowling and dismissed for 244 on Day 1.
Karnataka were 39 for no loss at stumps, with Ravikumar Samarath (21 not out) and Mayank Agarwal (15 not out) in the middle.
While the Rest of India lower-order did a decent repair job, the top-order couldn’t do much against the pace trio of R Vinay Kumar (3/76), Abhimanyu Mithun (3/46) and Sreenath Aravind (1/40).
Unmukt Chand lasted a delivery on Day 1 while his opening partner, Jiwanjot Singh (17), was dismissed early on Day 2. He tickled a regulation leg-side ball straight into the hands of wicketkeeper Naman Ojha.
The following period of play saw Ojha and Dogra defending against the Karnataka pacemen, who maintained a nagging off-stump line.
As it turned out, leg spinner Shreyas Gopal broke the 49-run stand by trapping Dogra leg before. Replays, however, showed that the ball hit his bat before striking the pad.
Ojha departed soon after and with the subsequent fall of skipper Manoj Tiwary (14), Rest of India were in a spot of bother at 102 for five.
The 80-run sixth-wicket stand between Jadhav and Yadav resurrected the innings and took the team closer to Karnataka's total before Mithun struck twice in the 63rd over, sending Rishi Dhawan and Jadhav back in the hut.
Aaron, who took a six-wicket haul on Tuesday, then eked out a 20-run lead for his team in a 52-ball stay.
Brief scores:
Karnataka: 244 and 39/0 in 11 overs.
Rest of India: 264 in 75.4 overs (Kedar Jadhav 78, Jayant Yadav 26, Naman Ojha 34; Vinay Kumar 3/76, Abhimanyu Mithun 3/46).
Image: Kedar Jhadav hits a boundary
Photograph: PTI
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