Uttar Pradesh, who had made 132 in their first innings in reply to the visitors' 184, were 77 for one at stumps on day two, needing 83 more to win the tie at the Kamla Club ground.
At close, Jyoti Yadav (26) and Suresh Raina (41) were at the crease.
Earlier, the home side resuming their first innings at 111 for five lost their remaining wickets for the addition of just 21 runs as Assam bowlers struck in quick succession. R K Yadav was the most successful bowler with figures of 6/57.
Assam, however, failed to cash in on the advantage as they lost wickets at regular intervals in the face of some fine bowling by R P Singh (5/35) and A W Zaidi (3/23).