Shikhar Dhawan was unbeaten on 49 and had Cheteshwar Pujara for company on 22.
New Zealand's lone success came when Murali Vijay tickled a delivery down the leg side from Tim Southee to wicket keeper BJ Watling for 13.
India's pace bowlers gave their side a slim chance of winning the Test after New Zealand were bowled out for a paltry 105 in their second innings.
That meant India required a mammoth 407 for victory but with more than two days to achieve the target.
Image: India’s Mohammed Shami celebrates bowling out New Zealand’s Corey Anderson for 2 on the 3rd day of the 1st cricket test at Eden Park in Auckland, New Zealand, Saturday, Feb. 8, 2014.