Chasing a mammoth target of 540, New Zealand were reduced to 140/5 at stumps on day three after India declared their innings on 276/6 at Wankhede.
With two days to go, India are now five wickets away from a win while New Zealand will need a huge miracle to make a game out of this as they are still 400 runs away from victory.
Ravichandran Ashwin ran through New Zealand's top four with three-wicket haul. Daryl Mitchell and Henry Nicholls showed some grit but two wickets towards the end of the day put India firmly in the driver's seat going into the penultimate day.
Earlier in the day, Mayank Agarwal led the way with a fifty while Cheteshwar Pujara, Shubman Gill, Virat Kohli and Axar Patel all made valuable contributions to take India to 276/6d.
Starting at 69/0, Cheteshwar Pujara began the day in style with back-to-back boundaries off the bowling of Ajaz Patel, eager to add to his ten-wicket haul in the first innings. Mayank Agarwal joined in for India, hitting a six and a four of his own in consecutive deliveries, bringing up a half century in the process.
Agarwal would fall for 62, with Ajaz taking his 11th wicket for the match, miscuing to Will Young. 11 became 12 for the left-arm orthodox spinner, claiming Pujara for 47 with a thick edge to Ross Taylor at slip.
Ajaz bowled 12 overs in the first session of day three, as Shubman Gill and Virat Kohli moved into a lead in excess of 400 at lunch.
After the break, the batters took the attack to William Somerville, with Kohli and Gill smashing a six each in consecutive overs.
Shubman Gill, who looked set for a big score, once again fell short of his fifty, with Rachin Ravindra bagging his maiden Test wicket. Shreyas Iyer made his intent clear as soon as he walked out to bat, clearing the ropes twice off Somerville's bowling, before he was stumped out by Ajaz Patel for a 8-ball 14.
India lost their third wicket in four overs when Kohli chopped on a ball from Ravindra for 36. Wriddhiman Saha too followed the captain back to the pavilion soon but it had no effect on the approach of Axar Patel, who used the left-arm angle of Ajaz and Ravindra to his advantage as he smashed them to all parts.
He was unbeaten on 41 off just 26 balls, an innings that include three fours and four maximums, when Kohli decided to declare after the wicket of Jayant Yadav, setting New Zealand a target of 540.
India got off to a perfect start, with Ravichandran Ashwin getting the better of Tom Latham for the eighth time in Test cricket, trapping him in front of the stumps for 6 as New Zealand went to tea at 13/1.
Siraj came out all guns blazing after the break and was breathing fire in the first two overs of the final session of the day. New Zealand went on the counter-attack soon and showed some intensity in a six-over period that saw Will Young and Daryl Mitchell score 29 runs that included six boundaries.
Ashwin struck twice in two overs to expose the middle order. Aswhin got one to spin and bounce sharply and caught Young on the backfoot, who inside edged onto the and pads into the hands of short leg.
Taylor uncomfortable stay at the crease lasted only six balls, as he mistimed a slog sweep that Pujara gobbled up a good catch running backwards.
Mitchell, in the company of Henry Nicholls, continued to take the attack to the bowlers and kept the scoreboard ticking by finding the ropes with regularity. Consecutive boundaries off Umesh Yadav first brought up the 50-run partnership of the pair as well as Mitchell's second Test fifty.
Axar Patel brought an end to the resistance between the fourth-wicket pair. Mitchell, who had hit the left-arm spinner for a six the previous ball, decided to take the aerial route but holed out to Jayant Yadav at deep cover.
Tom Blundell made the long walk back without disturbing the scorers. Trying to steal a single after playing it to mid-on, Blundell was halfway down the track when Nicholls sent him back. Bharat sent a good throw adjacent to the stumps and Saha whipped the bails off with the batter well short of his crease.
Rachin Ravindra and Nicholls saw off the remaining eight overs of the day, with New Zealand still 400 runs behind the target of 540 with only five wickets in hand.
