Pati struck a patient 94 and shared a crucial 132-run partnership with skipper Biplab Samantray (64 batting) for the fifth wicket at the DRIEMS Ground, Tangi.
Jharkhand had made 221 all out in their first innings from 67.4 overs.
Odisha added 208 runs today after resuming the day at 37 for one and they now have a first innings lead of 24 runs with five wickets remaining.
Pacer Varun Aaron broke the fifth-wicket partnership in the final session of the day when he had Pati caught by Shahbaz Nadeem.
Subhrajit Sahoo (3) was giving Samantray company on three at the draw of stumps.
For Jharkhand, Ajay Yadav was the pick of the bowlers with three for 48 while Aaron and Shankar Rao chipped in with a wicket each.
Odisha: 245 for 5 in 99 overs (Bikas Pati 94, Biplab Samantray 64 batting; Ajay Yadav 3/48).
