At close, the Kiwis had stretched their lead to 146 and were 107 for three in their second essay.
Earlier, resuming at 162 for three, M Vijay (overnight 76) and Pujara (overnight 49), built a strong 139-run fourth wicket stand.
However, Vijay's (98) departure triggered the collapse, as India fell from 195 for three in 78.1 overs to 276 all out in 119 overs.
Vijay, who was all set for a deserving hundred, spooned a catch to short cover of off-spinner McCullum. He scored 98 in 250 balls hitting 13 fours and two sixers.
Pujara (80, 201 balls, 5x4) too followed suit nicking medium pacer Ian O'Brien to wicket keeper Reece Young.
Ravindra Jadeja scored 33, before the lower order succumbed to off-spinner Aaron Redmond who claimed four wickets.
With a lead of 39 runs, the Kiwis lost opener Redmond (5) early. But fellow opener Martin Guptill 41 (77b, 7x4, 1x6) and skipper Peter Fulton, who scored a run-a-ball 33 (4x4, 2x6) put the innings on firm footing.
They fell in quick succession before Greg Hay and Marshall played out till the close.
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