Karnataka took a paltry 11 runs first innings lead after scoring 213 and then reduced Orissa to 255, giving the home side a target of 245 to win.
At close of third day's play, Karnataka were 43 for one, needing another 202 runs with nine wickets in hand to register their first outright victory of the current season.
Opener Robin Uthappa and Satish Ganesh were unbeaten on 25 and five respectively.
K B Pawan lost his wicket to Alok Mangaraj for 12.
Vinay emerged as the wrecker-in-chief with figures of seven for 58, while Akshay and Stuart Binny claiming two and a wicket each to shoot out the vistors in 74 overs.
Biplab Samantray top-scored for Orissa with a steady 138-ball 86, which was adorned with 13 fours. Other notable contributors for the visitors were Alok Sahoo (37) and Subhrajit Sahoo (48).
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For a brief period, Samantray and Sahoo gave a scare to the home side with a solid 100-run partnership.
Earlier, Orissa began at their overnight score of 30 for loss of two wickets and soon they were rattled by the pace of Vinay who hardly gave any chance for the batsmen to find their feet. The likes of Alok Sahoo (37) and Govind Podder (16) could not step up the fight.
Akshay gave able to support to Vinay at the other end and packed off Nataraj Behera to the hut for 17, leaving Orissa tottering at 142 for five at lunch.