Dhawan was unbeaten on 81 runs (152 balls, 9 fours) and Kohli was batting on 55 not out (82 balls, 10 fours) as the duo shared an unbeaten 84-run stand for the third wicket after Tim Southee had dismissed Cheteshwar Pujara (23) early in the morning.
Chasing 407 to win, India still need 227 runs with eight wickets in hand for a turn-around victory here.
In the very first over of the day, the former quickly moved on his half-century, getting the milestone ticked off early, facing 75 balls and hitting five fours in doing so.
It was his first half-century in five Test matches, since his maiden Test hundred versus Australia at Mohali nearly a year ago.
Even so, the start was shaky, with Dhawan surviving a couple of LBW shots, even if they seemed to be sailing over the stumps.
The Black Caps were bowling a nagging line and length, especially Tim Southee and he was soon rewarded for it. In the fifth over of the morning, 30th overall of the innings, he bowled a near-perfect delivery to Pujara who could do nothing but play at it and edged it the keeper.
Kohli then came out to bat and patiently saw off Southee's super spell of 6-3-4-1. At the other end, Dhawan too continued to bat cautiously as the 100-run mark came for the chase in the 32nd over. They tempered their batting according to the situation, mixing aggression with defence.
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