Mohanty grabbed all the six Jharkhand wickets that fell today as the visiting side ended the day at 149 for six at the DRIEMS Ground at Tangi here.
Saurabh Tiwary (57) and Pappu Singh (56 batting) were the only two Jharkhand batsmen who put up some resistance.
Jharkhand now lead by 63 runs with four second innings wickets in hand.
Tomorrow's first session may determine the outcome of the match. If Odisha are able to bundle out Jharkhand quickly, they may be able to force a win. Otherwise, the match may end in a draw as with a day remaining and just 63 runs ahead, Jharkhand are unlikely to force a win.
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Jharkhand continued their awful batting by being reduced to 37 for five before Tiwary and Singh shared 99 runs for the sixth wicket to save the visiting side from disaster.
Earlier, Odisha were all out for 307 in 118.4 overs after resuming the day at 245 for five.
Biplab Samantray could add just three runs to his overnight 64 as Odisha score 62 more runs today in 19.4 overs.
Jharkhand 221 & 149 for 6 in 59 overs (Saurabh Tiwary 57, Pappu Singh 56; Basant Mohanty 6/63).
Odisha: 307 all out in 118.4 overs (Biplab Samantray 67; Ajay Yadav 5/61).