In their second innings, Odisha scored 178 for five before the final day's play ended at the Maharashtra Cricket Association Stadium.
Maharashtra had responded with 371 all out after Odisha were bowled out for 311 in their first innings.
On the fourth day Natraj Behera, who had made 66 in the first-innings, top-scored for Odisha with a knock of 74 that came off 189 balls.
The opener struck eight boundaries during his 274-minutes stay at the crease.
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Earlier in the morning, Odisha resumed their second innings at an overnight score of 1 for no loss with Behera and Girija Rout in the middle.
Brief scores:
Odisha: 311 and 178 for five in 77 overs (Natraj Behera 74; Akshay Darekar 3/32).