Guptill, who is in poor form, tried to hit Ashwin down the ground and the ball bounced up off his boot to silly mid off; Latham went in similar fashion to the first innings, lbw to a ball which carried on with the arm.
New Zealand's senior batsmen, captain Kane Williamson and Ross Taylor, put on 40 without ever being in control against the formidable Ashwin, with large clouds of dust puffing up with every ball pitching.
Williamson, dropped at deep square leg on 16, went lbw to Ashwin, giving him his 200th test wicket. He got there at a quicker rate, 37 overs, than any other bowler in history apart from Australian legspinner Clarrie Grimmett of the 1920s and 30s, who got to 200 one game faster.
Taylor, who had been edgy throughout his innings, committed batting suicide. Coming back for a second run to Luke Ronchi, he failed to ground his bat in his crease and was run out by Umesh Yadav's direct hit from deep mid wicket.
With the crowd in uproar, and India sensing a chance to slice right through the innings, Ronchi and Santner dug in impressively.
Ronchi struck Ashwin for a six over long on and picked his moments to attack. Santner defended stoutly.
The likelihood is that it won't be enough to stave off defeat, but at least the pair have ensured New Zealand live to fight into the last day.
New Zealand did a tidy job of putting a plug on India's desire for rapid runs in the morning session, Santner and offspinner Mark Craig doing good, steady work, as New Zealand took three for 93 off 34 overs.
But Sharma and Jadeja got away and put the foot down in the second session.
Ashwin, in particular, and Jadeja were a handful for New Zealand, and unless rain intervenes, and a passing shower was anticipated today, India will take a 1-0 lead to the second test in Kolkata, starting on next Friday.
