Agarwal blasted four boundaries and three sixes in his 77-ball innings, while Vihari's 67-ball innings was laced with three fours and a six.
Arup Das (3/45) and Jogeswar Bhumiz (3/58) were the top wicket takers for Assam, while Krishna Das and Amit Verma also picked one each.
Put into bat,Hyderabad were off to a good start as Akshath Reddy (25) and Danny Prince (32) scored 56 runs in 14.3 overs for the first Wicket but Jogeswar Bhumiz sent the duo back to the hut with the score reading 66-2 in 18.4 overs.
Sumanth Kolla (34) and Agarwal then added another 44 runs before the latter was sent packing.
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Arup Das then dismissed Sumanth and B Anirudh (12) in the 47th over as Hyderabad eventually folded for 271 at the Gymkhana Ground.
Chasing 272 to win, Assam rode on opener Pallav Kumar Das's fifty to stay in the hunt till the 30th over but then they lost half their side for 142 for five in 30.4 overs.
The visitors then lost the plot as C V Milind dismissed Syed Mohammad (30) and Gokul Sharma (19) in the 38th and 40th overs respectively and the rest of the Assam batsmen also were back to the hut soon.
Brief Score:
Hyderabad: 271 for 8 in 50 overs (Tanmay Agarwal 83; J Bhumiz 3/58)
Assam: 199 allout in 50 overs (P Das 54; R Kiran 3/30).