Chasing 213 for a win, Jharkhand lost Manish Vardhan (10) and Ishank Jaggi inside the first 20 runs before first innings half-centurion, Rameez Nemat (37 not out) and Saurabh Tiwary (8 not out) held fort.
But the remaining Jharkhand batsmen will have to bat out of their skin as they require another 157 runs on a fourth day pitch at the Kennan Stadium, which has already started assisting the spinners.
Earlier, resuming at an overnight score of 27 for two, Assam rode on half centuries from Amit Sinha (55) and Tarjinder Singh (53 not out) to go past the 200-run mark.
Jharkhand skipper Shahbaz Nadeem (4/83) and off-spinner Sunny Gupta (3/69) knocked the stuffing out of Assam batsmen, scalping four and three wickets, respectively.
Brief scores:
Assam: 179 & 207 all out in 74.5 overs (Amit Sinha 55, Tarjinder Singh 53 not out, Shahbaz Nadeem 4/83, Sunny Gupta 3/69).
Jharkhand Ist innings: 174 & 56 for two in 11.1 overs (Rameez Nemat 37 not out, Jamaluddin Syed Mohammad 1/12).