Robin Uthappa top-scored with an unbeaten 83 off 181 balls, while opener Mayank Agarwal struck 78 off 149 balls as Karnataka took a lead of 23 runs with seven wickets remaining at the Srikantadatta Narasimha Raja Wadeyar Ground.
At stumps on day three, Karun Nair was giving Uthappa company on 52, which came off 130 deliveries.
Abhishek Reddy made 36 off 102 balls with the help of two fours and a six.
After Agarwal's departure with the team score reading 128 for three, Uthappa and Nair was involved in an unbeaten century stand, comfortably taking the team past the visiting side's total of 232 all out.
Uthappa hit seven fours and a six, while Nair found the fence thrice and cleared it once.