Captain Virat Kohli scored his second double century (211) and Ajinkya Rahane made 188 in a record Indian 365 run partnership for the fourth wicket as India piled on 557/5 before declaring on Day 2 of the third Test at Indore on Sunday.
Kane Williamson was New Zealand's key player at the start of the Test series, but the Kiwi skipper has failed to make a mark on this series, having been dominated by Ashwin.
Trent Boult was Ashwin's sixth victim of the day as he miscued a heave to Cheteshwar Pujara at midwicket to signal an end to New Zealand's innings, which ended 258 runs in the deficit.
The 27-year-old got ample support from his deputy Ajinkya Rahane (79 not out), who became the 36th Indian batsman to cross the milestone of 2000 Test runs during the innings.
Guptill had also played two streaky shots to the fence in the first hour and then an authentic back-foot punch to the covers off Yadav, easily the best shot of the first hour's play.
India had reached 456/3 at Tea on Day 2 of the third Test. India has already won the first two Test series held at Kanpur and Kolkata.
Ravi Ashwin's six wickets have put India in total control of the third Test after New Zealand were bowled out for 299 on day three. Turn and bounce caused Watling to glove to slip, while turn out of the rough found Santner's inside edge as he looked to drive out of the rough.
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Replying to India's mammoth 557 for five declared, New Zealand were in a steady position going into lunch at 125 for one but a sudden collapse in post-lunch session saw them lose four wickets between 43rd and 49th over leaving them reeling at 148 for five.
He was also responsible for running out Guptill and Jeetan Patel by deflecting the ball on to the non-striker's end stumps, as the batsmen were caught out of the crease.
Apart from Ashwin, left-arm spinner Ravindra Jadeja was the only other successful bowler among the Indians with figures of 1/48.
Martin Guptill was unfortunately run out as Ashwin fielded the ball of his own bowling and it went on to hit the stumps.
Bradley-John Watling (23) and Neesham then tried to bring the Kiwi innings back on track with a 53-run partnership.
"I think New Zealand has definitely batted well". Spin was introduced as early as the fifth over and Ashwin and Jadeja operated in tandem.
After the tea break, it was a one way traffic for India as both the spinners lost little time in taking the remaining four wickets before Kohli opted against enforcing the follow-on.