Skipper Dhawan led from the front with figures of 13-5-29-5, while his pace partner V S Malik (3/24) took three wickets and Akshay Chauhan (2/23) accounted for two at the Himachal Pradesh Cricket Association Stadium here.
Himachal have already taken 118 runs first innings lead with six wickets remaining.
For Assam, only three batsmen -- Niraj Patel (17), J Syed Mohammad (17) and Dheeraj Jadhav (13) -- reached the double digits after they were put in to bat.
In reply to Assam's first innings score, Himachal batsmen batted with a lot of responsibility and almost everyone in the top and middle order contributed to the team's cause.
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Although all of them wasted their good starts as they lose their wickets after reaching 30s and 40s.
At stumps, Nikhil Gangta was unbeaten on 43 and giving him company at the other end was Rishi Dhawan on 36.
Brief scores:
Assam 1st innings: 81 all out in 32.5 overs (Niraj Patel 17, J Syed Mohammad 17; Rishi Dhawan 5/29, VS Malik 3/24).