The 29-year-old snapped a 21-month string of low scores and survived multiple dropped catches for his sixth Test century.
India vs New Zealand: Trent Boult says Hagley Oval pitch will offer more assistance to seamers than Basin Reserve Track
Boult also gave indications that Kyle Jamieson, after his match-winning all-round performance at the Basin, will be preferred over left-arm orthodox bowler Ajaz Patel
Agarwal (34) was the only batsman, apart from vice-captain Ajinkya Rahane (38 batting), who was able to counter the New Zealand seamers as India scored 122 for five in the rain-marred first day.
India vs New Zealand 1st Test in Wellington weather update: Overcast conditions, late showers expected on first three days
Here is the weather update for the first Test match between India and New Zealand that begins on 21 February at Basin Reserve in Wellington
India vs New Zealand: Indian openers inexperienced but still class players, says Black Caps pacer Tim Southee
With Rohit Sharma ruled out due to hamstring injury and KL Rahul not selected, the onus is on Shaw (2 Tests) and Agarwal (9 Tests) to give India a good start against the likes of Trent Boult, Tim Southee and Matt Henry in the series beginning on Friday.
The downpour which had persisted for a day and a half stopped long enough on day two for the covers to be lifted and for the players to start warming up.
Highlights, New Zealand vs Sri Lanka, 1st Test at Wellington, Day 3, Full Cricket Score: Black Caps sniff victory after early wickets
Follow live updates on Day 3 of the first Test between New Zealand and Sri Lanka at Wellington's Basin Reserve.
Opener Tom Latham's unbeaten century put New Zealand in charge of the first Test against Sri Lanka in Wellington on Sunday, as the Black Caps raced past the tourists' first-innings total and looked to build an imposing lead.
New Zealand vs Sri Lanka: Visitors fight back after Tim Southee's destructive spell to reach 275/9 at stumps
Paceman Tim Southee skittled Sri Lanka's top order with a five-wicket haul to put New Zealand in a commanding position on the opening day of the first Test in Wellington on Saturday.
New Zealand vs West Indies: Matt Henry to replace Tim Southee for 1st Test, confirms captain Kane Williamson
Although Ferguson took seven wickets for New Zealand A against the Windies earlier this week, Williamson said Henry had been playing well for a long time.
Adam Voges is revelling in his luck after a game-breaking 239 against New Zealand following an umpiring blunder in the first Test in Wellington
Will Baz get the perfect send-off? McCullum hopes to cap 100th Test with series win against Australia
NZ captain Brendon McCullum wants to break a 26-year-old jinx by recording a Test series win against Australia
Fifteen wickets fell in a bowlers' blitz Saturday as Sri Lanka ended the first day of the second Test in Wellington at 78-5 in reply to New Zealand's first innings 221.
Statistical highlights on the fifth and final day of the second cricket Test between India and New Zealand here today.
The unbroken 125-run partnership between Brendon McCullum and Neesham is New Zealand's highest stand against India at Basin Reserve, Wellington in Tests.
The hosts took a 325-run lead at the end of the fourth day's play at Basin Reserve, with skipper Brendon McCullum scoring an unbeaten 281. But Dhawan chose to stay positive after what was a throughly disappointing day for Indian bowlers.
BJ Watling came in at 94/5 and put on that record stand to defy the Indian hopes.
The long-term effectiveness of his attacking play remains to be seen – failures are inevitable with this strategy - but for now India will take runs however Dhoni makes them.
"Rahane has always been very willing to put in the hard yards. He simply never takes it easy. "