Sharma (6/51) justified captain MS Dhoni's decision to bowl first on a greentop as the lanky pacer kept the host batsmen on their toes with his testing line and length.
Rising pacer Mohammad Shami (4/70) also contributed in India's dominating performance show on day one as he picked up key wickets of Kane Williamson (47) and debutant James Neesham (33) at crucial junctures.
Dhawan (71) and night-watchman Sharma (3) were at the crease after the visitors lost the wickets of opener Murali Vijay (2) and Cheteshwar Pujara (19).
Sharma continued with his splendid show from the first Test as he claimed his second five-wicket haul of the series and fifth overall in his 55th Test.
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Sharma took three wickets in the first four overs of his morning spell and that laid the foundation for India's hugely successful day when they are hoping to level the series.
It meant that Sharma was introduced into the attack as early as the eighth over and thereon, went on to bowl unchanged for nine overs, turning the morning session India's way.
Hamish Rutherford (12) was unable to keep down a well-aimed short ball and was caught by Vijay at first slip. Two overs later, Sharma bowled an inswinger that hit Peter Fulton (13) on his pads and was trapped LBW, resulting in another poor start for the Kiwis.