They attacked when the game was long off the line, the pressure was off.
Making India follow on, a big second innings score was always a strong chance, but I don't envy the decisions that Vettori had to make. When India were bowled out, they were at the end of day 3 and batting would not have looked all that enticing with a shaky top order. They also had two full days to bowl India out and it would have looked as though they could just be ground out of it. Alas, as is so often the case with following on and during long innings, the bowling team just fell further and further away.
Of course, the alternate route was still fraught with danger. Had NZ only added 100 or so, India may well have come away with a seeming gift of a win, but had they stacked on another 200 to reset India behind a mammoth total, would the game have been any more contentious? One can estimate that they would have batted to lunch on day 4, or maybe after lunch given India's over rates. At the rate that they have scored, India would still be yet to reach 400, so it would have been even easier to commit to a draw, but maybe also easier to commit to a win knowing NZ could not bat again. It may only have taken the cheap removal of Gambhir and Dravid to bring the game right under NZ's thumb.
Although a draw does nothing for the home side, being 1-0 down, it's definitely a confidence victory for them. They batted better than they might have thought they could and they generally bowled better than India, who might feel like they lost ground in failing to dominate on an excellent batting surface. If the Basin has a little more in it for the seamers, it could make for an interesting conclusion to a series that would otherwise have looked to be no contest.