New Zealand were tottering at 93 for four in their second innings with the exuberant Luke Ronchi (38) and the steady Mitchell Santner (8) at the crease when stumps were drawn on the fourth day.
The Black Caps require a history-defying effort to win the Test as no team has ever chased such a daunting target. They still need 341 runs and batting three sessions on a fifth-day wicket is not something visiting teams have achieved often in India.
Left-arm spinner Mitchell Santner dismissed two batsmen while Ish Sodhi and Mark Craig claimed a wicket apiece but only to see the next Indian pair hammer them around the park as India declared their second innings at 377 for five at the stroke of tea.
Rohit and Jadeja never looked uncomfortable on the deteriorating fourth-day Green Park track, entertaining the Sunday crowd with some quality strokes, including three sixes by the left-hander.
Guptill was first to go by handing an inside edge to forward short-leg fielder while left-handed Latham was caught in front of the wicket while defending.
Ashwin could have got Kane Williamson (25), when he was on 16, had Umesh Yadav held on to a tough chance at square leg boundary but the off-spinner did not have to wait for long to see the back of the New Zealand captain as he trapped him soon and completed a milestone of 200 Test wickets.
Ashwin is the second fastest in the world behind Australian Clarrie Grimmett (36 matches).
(REOPENS DEL 46)
Ronchi had pushed the ball through covers and there was no scope of a run out. However, Yadav's direct hit converted it into a wicket out of nothing. Taylor would certainly rue the silly mistake.
This happened after Ashwin saw a second chance grassed by the fielder off his bowling. Ronchi (on 3 at the time) drove him uppishly, edged the ball high in the air, but Murali Vijay could not catch it while running backwards.
They raised an unconquered 100-run stand for the sixth wicket and the moment Jadeja got a single off Santner to get to his half-century, Indian captain Virat Kohli declared and umpired called the tea break.
Jadeja celebrated his milestone by wielding his bat like a sword before the two batsmen walked off the field. Rohit and Jadeja played in contrasting fashion with the left-hander being more aggressive even as they scored 125 runs in the second session after Rahane was trapped by Santner.
Except for two overs, Williamson had his spinners operating from both ends and each one of the three spinners delivered a wicket apiece.
Vijay and Pujara batted for about 10 overs together before Santner broke the 133-stand between them by trapping the former. Vijay played for turn, missed and the ball struck his pad before hitting the outside edge of his bat. He could add only 12 runs to his overnight total.
Later Saha was out leg before in the last over before tea
to complete a miserable second session for the home team.
Australia, ahead by 155 runs on the first innings, were dismissed by the hosts for 285 in the extended first session.
India's highest ever successful fourth innings run-chase at home has been 387 against England in 2008 at Chennai.
The visitors added 142 runs in the extended opening session in 41 overs after commencing at the overnight 143 for 4 with Smith (59) and Mitchell Marsh (21) at the crease.
However, by the time of the visiting team's skipper departure at 246 the Australian lead had swelled past the 400 mark - a huge one by any reckoning that looks impregnable on this treacherous pitch.
Mitchell Starc, who made a whirlwind 61 in the first innings, later treated the bowlers harshly by striking 3 sixes and 2 fours in a quick-fire 30 off 31 balls before he was caught in the deep off Ravichandran Ashwin to give the off spinner his first wicket of the day and fourth overall.
Umesh Yadav, the only other successful bowler, finished with 2 for 39 to add to his 4 for 32 in the first innings.
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