In the post-lunch session, after loss of two wickets, Williamson and Taylor have kept the Indian bowlers at bay as the hosts just trail by 49 runs and are looking good for a sizeable first-innings lead.
Meanwhile, Ross Taylor received a standing ovation from the Basin Reserve crowd as he walked out to bat in his 100th Test match.
New Zealand took control of the first Test after bowling out India for a paltry 165 on the second day. At Lunch on Saturday, New Zealand were 17/0 and are trailing by 148 runs with Tom Latham and Tom Blundell batting on 11 and 6 respectively.
Earlier, debutant pacer Kyle Jamieson and Tim Southee came out with splendid bowling performances as India lost their last five wickets adding just 41 runs to their overnight score.
Resuming the day at 122/5, the visitors lost Rishabh Pant very early in the morning as he got run-out after adding just nine more runs to his overnight score of 10.
Ravichandran Ashwin, who came in next, couldn't stay long at the crease and was sent back on the very first ball by Southee.
Vice-captain Ajinkya Rahane, who was holding India's hopes for a big score, also failed to add much and became the third scalp of Southee after contributing with 46.
However, Mohammad Shami did play a nice, little cameo towards the end of the innings and contributed with valuable 21 runs to help get the team past the 150-run mark.
However, he didn't find much support from Ishant Sharma and Jasprit Bumrah who could manage just 5 and 0* respectively.
While Southee returned with figures of 4/49, debutant Jamieson was the pick of the bowlers as he also scalped four wickets giving away 39 runs in his 16 overs.
New Zealand openers Blundell and Latham then played out the remaining eight overs with utmost caution and made sure the hosts didn't lose any wicket in the morning session.
They played with patience against the quality pace trio of Ishant, Bumrah and Shami and didn't allow India get a breakthrough.
(With IANS inputs)