Dravid (191) fell nine short of a double century as the home side declared on 566-8, giving them a lead of 373 after they restricted New Zealand to a first innings score of 193.
Resuming on 292-2, India lost Sachin Tendulkar (61)Ã¢â‚¬â€who was searching for his 50th Test centuryÃ¢â‚¬â€after he edged to wicket-keeper Gareth Hopkins off the bowling of debutant Andy McKay.
VVS Laxman (12) and Suresh Raina (3) soon followed as New Zealand fought back during the morning session.
But a 193 sixth-wicket stand between Dravid and captain Mahendra Singh Dhoni (98) put India back in control just when the visitors thought they might be getting back into the contest.
Singh fell two short of his fifth Test century when he hit a lofted delivery back at Daniel Vettori to leave the New Zealand captain with an easy catch.
Ten overs later Dravid fell when he was caught at long on by Martin Guptill off the bowling of Kane Williamson.
After Harbhajan Singh (20), who had scored centuries in the last two games, lost his wicket to Chris Martin, Dhoni decided to declare with 11 overs of play left.
New Zealand closed on 24-1 after Harbhajan trapped opener Tim McIntosh lbw for eight. Brendon McCullum (15) and night watchman Hopkins will resume tomorrow with the visitors needing 350 to avoid an innings defeat.
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BIOGRAPHY: Marcus Rashford