While Gambhir looked good during his innings of 29, other opener Murali Vijay was out for 10 in the first session.
Vijay fell to off-spinner Jeetan Patel in the fifth over as his flick was taken by Jeetan Patel at forward short-leg.
Gambhir started off well and played some audacious pull-shots before going into a defensive shell as Trent Boult trapped him leg-before in the 20th over.
Choosing to bat first, India began confidently with the new opening combination of Vijay and Gambhir. The Delhi left-hander, playing his first game since losing his spot after the away defeat to England in 2014, did not appear to be in any sort of trouble on a placid track.
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Gambhir, playing with a changed and more open stance, began with a rasping square cut four off Matt Henry in the second over while Vijay played a couple of pleasing drives on the off-side against left-arm Trent Boult for fours in the next over.
With the pacers not making any impression on the two Indian openers, New Zealand captain Kane Williamson, who is back in the side having recovered from the viral infection, introduced spin by bringing into the attack Jeetan Patel.
The move paid immediate dividends albeit through a fine, juggling catch by Latham at forward short leg when Vijay played his pet flick off the front foot. It was Vijay's third failure in the series.
The second wicket duo played spin with calm assurance, and Williamson brought back his pace duo to try and get another wicket.
Pujara struck Henry for two fours in successive balls, the second one off an edge, to raise the 50 of the innings in the 13th over. He survived a close leg before the wicket appeal soon afterwards off Boult, the ball striking him on pads just outside the line of off stump.
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