The Indian bowlers struggled to build pressure in the first session of the day, despite taking four wickets before the lunch interval.
Corey Anderson (77) fell short of a century but Brendon McCullum (224) continued to punish the tourists by recording his second double hundred in Test cricket in the final over of the opening session.
New Zealand were eventually dismissed for 503 and they quickly made a breakthrough with the ball as India's reply started disappointingly.
However, New Zealand were able to take one more wicket in the final session when Neil Wagner beat Vijay's defence to dismiss the opener.
Sharma and Ajinkya Rahane (23*) were left at the crease when bad light in Auckland ended the day prematurely with India on 130-4, trailing the hosts by 373 runs.