Paceman Umesh Yadav then quickly trapped Tom Latham (six) lbw to leave the hosts needing nine New Zealand wickets in four sessions to complete a 3-0 series sweep.
New Zealand were 38 for one at tea on the fourth day with Martin Guptill (eight) and skipper Kane Williamson (23) in the middle, the tourists needing 437 more runs for an improbable victory.
Earlier, Gautam Gambhir struck 50 on his test return and Pujara remained not out on 101 as India declared their second innings on 216-3 around an hour before the tea break.
Resuming on 18-0, the hosts lost their first wicket when opener Murali Vijay was run out for 19 after aborting a quick single but Gambhir returned to the crease and scored fluently.
Injuries to openers Lokesh Rahul and Shikhar Dhawan prompted Gambhir's return to the test arena after a two-year absence and the southpaw initially failed to capitalise with a patchy first innings score of 29.
Things looked worse for Gambhir on Monday when he retired hurt with an injured shoulder but the Delhi player walked back out to bat after Vijay's exit.
Gambhir hit six boundaries before completing his 22nd test fifty off 54 balls but was dismissed when he drove off-spinner Jeetan Patel straight to Guptill at cover.
Patel dismissed home captain Virat Kohli (17) lbw for the second time in the match but Pujara and Ajinkya Rahane (23 not out) added 58 quick runs before Kohli called them in.
Pujara's hundred, to go with his three fifties in the series, included nine boundaries.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
