At Lunch on Saturday, Cheteshwar Pujara and Virat Kohli remained unbeaten at the crease on 15 and 3 respectively as India reached 85/2.
Earlier, the start of the match was delayed due to a light drizzle.
Kohli once again lost the toss and was put into bat by Kane Williamson in bowling-friendly conditions.
Mayank Agarwal and Shaw provided Indian with a quick start and collected 30 runs from the first five overs. However, Agarwal, who was among the runs in Wellington, couldn't stay long this time around and was trapped in front by Trent Boult after scoring just seven.
Despite losing his opening partner, 20-year-Shaw didn't deter from playing his attacking mode of cricket and along with Pujara, saw off the difficult period wherein all the New Zealand pacers bowled on probing lines.
Shaw kept on scoring boundaries and never let the hosts build pressure.
Both stitched a 50-run stand for the second wicket during the course of which Shaw scored his first fifty on foreign soil.
However, just when India appeared to be taking the advantage, Shaw became the victim of brilliance shown by Tom Latham at slips.
Latham took a brilliant, one handed catch off the bowling of Kyle Jamieson to dismiss Shaw at 54.
Kohli, who came in next, then made sure India didn't lose any further wickets till the end of the session and played with patience.
Brief scores: India 85/2 at Lunch (Prithvi Shaw 54, Cheteshwar Pujara 13*; Kyle Jamieson 1/18)