At stumps, Deepak Chahar was batting on 13 and K Ajay Singh was on six.
Earlier, resuming on 270 for eight in their first essay, Karnataka could add just another 11 runs to their overnight total, getting all out for 281.
Aniket Choudhary finished with best figures of five for 77 for Rajasthan.
In reply, Rajasthan were struggling at 48 for four before Bhatia came to the team's rescue.
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But at the end, Bhatia got out, falling just one short of a well deserved hundred.
R Vinay Kumar (2/39) and David Mathias (2/41) picked up two wickets each.
Brief scores:
Karnataka 1st innings: 281 (Mayank Agarwal 66, Ravikumar Samarth 65; Aniket Choudhary 5/77).
Rajasthan 1st innings: 219 for seven (Rajat Bhatia 99; R Vinay Kumar 2/39, David Mathias 2/41).