New Zealand need a further 159 runs just to make India bat again and face the prospect of losing the game inside three days.
Debutant Tom Latham was dismissed by Mohammed Shami in the final over before lunch for 29, having avoided the dreaded pair in his first test when he punched Zaheer through point for two runs.
Captain Brendon McCullum was on 14 at the break with Corey Anderson to join him afterwards.
India must win the match to level the two-test series after New Zealand won the first game at Eden Park by 40 runs and with the veteran Zaheer fired up they seemed keen on achieving victory on Sunday.
The 35-year-old left-armer had the ball move slightly away off the seam to catch the thinnest of outside edges of both Kane Williamson (seven) and Hamish Rutherford (35) to reduce the hosts to 52 for three inside the first hour.
Latham and McCullum buckled down to see the hosts almost through to the break before Dhoni took his third catch of the innings on the first ball of the final over before lunch.
India had been bowled out for 438 on the second day with Ajinkya Rahane scoring his maiden test century.
The compact right-hander top-scored with 118 and shared in profitable partnerships with Virat Kohli (38) and Dhoni (68), while opener Shikhar Dhawan scored 98.
New Zealand were dismissed for 192 on the first day.
(Editing by Amlan Chakraborty)
