In reply to Bengal's 419, Himachal, the Group D leaders, were bundled out for 206 in their first innings with Dinda grabbing 5/61 and complemented well by Shami (3/94) as the hosts enforced a follow-on in the first session.
Bengal, however, could not capitalise on their big 213- run first innings lead on an innocuous Eden wicket as Himachal ended the penultimate day at 207 for 2 when bad light stopped play in 58 overs.
Pressed into action, Shami dismissed skipper Sumeet Verma for a duck with an addition of four runs but before they could make further inroads, Khanduri and Nikhil Gangta (43 batting; 6x4s) showed fine application to end day three without further damage.
Continuing his fine run in his debut season, Khanduri struck his second successive half-century of the match and braved a furious spell from Shami with the ball staying precariously low.
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Khanduri, who has a century against Goa, found fine support from Gangta, fresh from back-to-back centuries in their last two matches as they put on an unbroken 78-run partnership for the third wicket to reduce the deficit to six runs.
Earlier, resuming the day with 256 runs in arrears Himachal managed to add 43 runs to their overnight total as their remaining five wickets could not stand against the fury of Dinda and Shami and their first innings folded in 56.2 overs.
With pace and swing, Shami moved the ball from good length, while Dinda generated awkward bounce off the track in a fine seam bowling display in the morning session.
It was Dinda, who gave the first breakthrough of the day when Ankush Bains (5) edged one to Abhimanyu Easwaran at the second slip.
Having troubled the batsmen with his pace and swing, Shami finally got his due sending Rishi Dhawan's offstump cartwheeling after the Himachal batsman dragged the ball in.
Dinda then scalped the wickets of Pankaj Jaiswal and Gurvinder Singh to register his 24th first-class five-wicket haul, while Mukesh Kumar wrapped it up after trapping Amit Kumar.
In Kolkata: Bengal 419 vs Himachal Pradesh 206 in 56.2 overs (Sumeet Verma 64, Priyanshu Khanduri 52; Ashoke Dinda 5/61, Mohammed Shami 3/94) and f/o 207 for 2 (Prashant Chopra 81, Priyanshu Khanduri 67 batting, Nikhil Gangta 43 batting).
In Nagpur: Vidarbha 385 & 111 for 2 in 28 overs (Faiz Fazal 46) vs Services 317 in 113 overs (Nakul Verma 71, Rahul Singh 63, Ravi Chauhan 44; Akshay Wakhare 5/87).
In Raipur: Chhatisgarh 238 & 171 for 4 in 64 overs (Ashutosh Singh 81 batting) vs Punjab 653 for 9 declared in 128.1 overs (Anmolpreet Singh 267, Gurkeerat Singh 111, Jiwanjot Singh 75; Shourabh Kharwar 3/107, Prateek Sinha 3/121).