In reply to India's first innings total of 316, New Zealand were still trailing by 231 runs when rain stopped play with 40 minutes to go for the scheduled tea break.
New Zealand stand-in skipper Ross Taylor (30) was at the crease after in-form Luke Ronchi just departed for 35 being adjudged lbw to Jadeja to a dubious decision.
Ronchi was trapped on his backfoot from an angled delivery from Jadeja which seemed to have gone down the leg but umpire Rod Tucker had other ideas as he gifted India another opening.
In fact, Ronchi's innings almost ended at 16 but he was dropped at point by substitute Gautam Gambhir who seemed slow to react and let down a regulation catch.
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Earlier, youngster Nicholls who replaced skipper Kane Williamson in the side dragged a widish delivery onto his stumps in a replay of Shikhar Dhawan's dismissal as India kept taking regular breakthroughs.
In reply to India's 316, New Zealand lost Tom Latham (1) and Martin Guptill (13) in successive overs with Shami and Bhuvneshwar taking the wickets.
Shami struck in his first over to dismiss Latham for LBW, while Guptill continued with his woeful run to be bowled by Kumar when the ball hit his elbow before crashing on to the stumps.
Earlier attacked by a barrage of short-pitch deliveries, Saha stood determined as he built his innings from being 14 not out last night to remain 54 not out, only the third half-century of his career as India made impressive progress from the overnight score of 239 for seven in 86 overs.
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The two local lads -- Saha and Shami -- shared 35 runs for the last wicket which came in just 31 balls before the latter was dismissed by a sharp sideway running catch by Matt Henry at fine leg to bundle out India in 104.5 overs.
Jadeja looked to break free after stepping out to left-arm spinner Mitchell Santer for a six in the previous over but Wagner set him up brilliantly as he pulled a straight catch to Henry at fine-leg for the day's first dismissal.
India were soon reduced to 281 for 9 but Saha and Shami ensured that the hosts get past the psychological 300-run mark in a last wicket partnership.
Saha came back strong and replied with a delicate boundary dissecting the packed slip cordon as India went past 250.
At the other end, Jadeja, who was yet to open his account, had a testing time from the three Kiwi pace lineup of Henry, Trent Boult and Neil Wagner.
India lead the three-match series 1-0 with their massive 197 runs victory in the first Test in Kanpur.