Resuming at 307 for five after a 26-minute delay because of bad weather, India gained from the partnership between Pujara and Dhoni who put on a fine 127-run partnership for the sixth wicket.
Pujara was dismissed in the post-lunch session after his brilliant innings of 159 (306 balls, 19x4, 1x6).
Dhoni gave him fine support at the other end with a 73 (147 balls, 6x4, 1x6), the skipper's 25th half-century in 68 Tests.
Ravichandran Ashwin chipped in with a 54-ball 37 (5x4) and shared a 24-run stand with the Dhoni before the skipper got out.
India were bundled out after Umesh Yadav ran himself out just ahead of the tea break.
Off-spinner Jeetan Patel became the visitors leading wicket-taker with 4/100, while Trent Boult scalped 3/93.
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The hosts, playing their first match after the retirement of Rahul Dravid and VVS Laxman, were in no trouble against the weak New Zealand attack as Pujara carried on from where he left yesterday.
Unbeaten on an overnight score of 119, his maiden century in four Tests, Pujara cleverly rotated the strike.