The Kiwis are still far from safety but they have wiped off the 246-run first innings deficit and taken a slender six-run lead.
Carter praised McCullum (114 not out) and Watling (52 not out) for their performances on day three, wherein they put on 158 runs for the sixth wicket to defy the visitors.
"The key for us was to have a partnership. We were really struggling in the morning. This was a real test of us today and tomorrow is the same - test of our batting to see whether we can put a score on the board in order to put India under pressure.
"They are a fine team, they are going to come out and bowl well again tomorrow. We know we have got a challenge on our hands, and it is something we are really looking forward to," he added.
"Brendon has now combined a lot of his game with defence. Today was a tough day of Test cricket. They didn't give us anything and they bowled well since they bowled in the second innings in Auckland. They bowled very well in this game. Brendon has really shown his defensive game is to come forward.