The United States on Monday accused Beijing of carrying out the cyber attack on Microsoft and charged four Chinese nationals over the "malicious" hack in March
Tim Southee took wickets at both ends of the innings on his way to 4-48 in 19 overs, with Rishabh Pant (41) the only India batsman to manage a score above 30.
Shami removed Ross Taylor and BJ Watling, either side of Ishant Sharma dismissing Henry Nicholls, to leave New Zealand still 82 runs behind India's first innings 217 at lunch on the fifth day.
Only 141.1 overs out of 360 scheduled for the first four days had been bowled, with New Zealand 101-2 in reply to India's first innings 217 -- a deficit of 116 runs.
"With the conditions, a bit of weather around, hopefully we can make the most of it first up, get a bit of seam movement," Williamson said at the toss.
New Zealand and India are the top two teams in the Test rankings but Kohli said that a one-off game would not give a definitive answer as to who was the best.