India, who elected to bat in the historic 500th Test, were on the top of the game in the morning but were put on the back-foot by the Kiwis in the post-lunch session during which they also got the crucial wicket of Indian captain Virat Kohli (9).
Left-arm spinner Michael Santner, who removed the in-form KL Rahul before lunch, got rid of Pujara while Neil Wagner saw the back of Indian captain Kohli.
Vijay, who shared a 112-run stand with Pujara, was patient from one end, treating the balls on merit. For someone, who was in and out of the side during the West Indies tour and scored only seven runs on the Caribbean soil, it was a good opportunity to get a big one.
Despite it being a first-day pitch, the ball has started doing a bit for the spinners and it was not a surprise that of the 59 overs so far, 37 have been bowled by three Kiwi spinners.
Vijay and Pujara continued in their nonchalant way in the post-lunch session, untroubled by the Kiwi bowlers.
Vijay guided Trent Boult to third man with a late cut to touch 49 and survived an LBW appeal off Sodhi before reaching his fifty with a single off Boult in the next over, the 41st of the innings.
Pujara also completed his half-century by driving Sodhi straight after getting a couple off the same bowler.
Vijay preferred to play his shots from the backfoot against both Sodhi or Boult while Pujara was impressive with his nimble footwork.
Wagner did get a bit of reverse swing but the well-set Indian batsmen dealt with it without fuss.
Santner provided the breakthrough again but it was a soft dismissal as Pujara lobbed one back to the bowler, attempting a straight shot. It was the kind of mistake Kiwis were hoping for and Pujara provided them the window.
(REOPENS DEL 27)
In came Kohli to the rapturous chants of his name and got to business straight away, cutting a widish Santner ball to the boundary ropes before pulling Wagner for a leg-side boundary.
Vijay was patient in his approach and helped himself with four shots to the fence while Pujara was swift and scored at a decent pace, hitting five boundaries.
Earlier, Rahul made a cracking start, hitting two crisp boundaries off Boult in the very first over. Wagner kept banging it short to test the Indian openers while Boult preferred a fullish length.
Rahul was confident and comfortable at the crease and never looked like troubled by either of the two fast bowlers.
It was a little quicker off the pitch, Rahul's hurried defence resulted in an edge, and Watling took a sharp catch.
Encouraged by the success of a spinner early in the innings, Williamson brought in off-break bowler Mark Craig.
Pujara, coming into the match on the back of a first-class double century, was confident on both sides of the wicket and used his feet to work the ball around.
Craig, a few times bowled from wide off the crease, but the Indians were hardly troubled.
India chose to field only two spinners - R Ashwin and Ravindra Jadeja - and two paceman - Umesh Yadav and Mohammed Shami - going in with seven batsmen.
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