India had resumed on 122-5 after the entire final session of the first day was washed out after heavy rain swept across the ground seconds after the players had taken the tea break.
Ajinkya Rahane resumed in brilliant sunshine on 38 while Rishabh Pant was with him on 10.
They started with a bang as Pant dispatched the fourth ball bowled by left-arm spinner Ajaz Patel out of the ground for the first six of India's innings.
Patel, however, got his revenge less than 10 minutes later when he ran the wicketkeeper out with a direct hit from point after Rahane had called Pant through for a single that was never on. Southee then bowled Ravichandran Ashwin on the next ball.
Southee then had Rahane caught by wicketkeeper BJ Watling from an under edge for 46 and finished the innings off when Mohammed Shami was caught by Tom Blundell for 21.
New Zealand pace bowler Kyle Jamieson had a dream test debut on Friday when he took three wickets, which included Cheteshwar Pujara and Virat Kohli, and had Ishant Sharma caught behind for five on Saturday to finish with 4-39.
In response, New Zealand made it through to lunch unscathed.
India lost a review for LBW against Tom Blundell as replays showed the ball taking a thick edge before hitting his pads.
The Black Caps will resume at 17/0 after the lunch break.
