At stumps, Odisha had taken a 16-run lead with six wickets remaining.
Going into tomorrow's game, Karnataka will be looking to bundle out the visitors as early as possible and then try to overhaul the required target to score an outright win.
Resuming on 288 for four with yesterday's centurion Manish Pandey and CM Gautam at the crease, Karnataka went on to add another 91 runs.
Gautam (16), who added 48 runs for the fourth wicket with Pandey, soon got out, but Pandey, who resumed on 108, scored a patient 132 off 236 balls, laced with 15 fours and four sixes.
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Odisha, in their second innings, got off to a disastrous start with their top order back in the pavillion with scorecard reading 36 for three.
Govind Poddar and skipper Biplab Samantray tried to steady the boat a bit but the former fell for 74-ball 34.
Samantray, however, found an able partner in Abhilash Mallick and the duo stitched an unbeaten 95 runs together for the fifth wicket at the draw of stumps.
It was HS Sharath (3/41), who accounted for all the three Odisha wickets on the day.
Brief scores:
Odisha: 226 & 169 for four in 60 overs (Biplab Samantray batting 50, Abhilash Mallick batting 47; HS Sharath 3/41).
Karnataka 1st innings: 379 all out (Manish Pandey 132, Abhimanyu Mithun 43; Suryakant Pradhan 3/66).