Karn Sharma and Swapnil Singh bag four key wickets to secure a 35-run victory in Hyderabad
Rory Burns (101) also scored his second Test century and combined with his captain in a 177-run third wicket partnership that resurrected England's first innings.
Root, who had not scored a Test century since early February and was averaging just 27.10 this year prior to his current innings, was on 114 at stumps with Ollie Pope on four and England within striking distance of New Zealand's 375.
Rain had forced the players off the field at about 5.30pm (0430 GMT) and umpires Kumar Dharmasena and Paul Wilson decided to abandon play 15 minutes later.
The final two days of the match are also expected to be affected by rain, increasing the chances that New Zealand will win their fifth successive Test series at home in the last two years after they won the first game by an innings and 65 runs.
"I think the game is reasonably even," New Zealand pace bowler Tim Southee told the BBC. "The ball is still reasonably hard.
"Hopefully we can turn up tomorrow, grab some assistance early and knock a couple over ... especially Root - then who knows?"
Root (84) and Ben Stokes (10) had resumed the final session on Sunday on 218-3 and were aggressive against the second new ball, which had been taken just before tea.
Stokes, however, was caught by first slip Ross Taylor off Southee for 26 just before Root brought up his century.
The England captain reached the milestone with successive boundaries off Neil Wagner in the next over.
He moved from 95 to 99 with a leg glance and then to 103 with an under edge that bounced over the stumps and past wicketkeeper BJ Watling's head for his 13th four.
Debutant Zak Crawley lasted just six balls, during which he survived a close run out as he scored his first Test run. He was caught behind by Watling off Wagner for one.
Burns was the only wicket to fall in the first two sessions when he was run out two balls after he reached his century.
He flicked a delivery from Wagner to the leg side and jogged a single but was then called through for a second run by Root and despite almost making his ground he was unable to beat Jeet Raval's flat throw from midwicket.
"I thought when Rooty asked me straight away, I was there," Burns told Britain's Sky Sports. "I thought I had enough in the tank but I wasn't quite there.
"Rooty was giving me a nudge and I thought 'go on then', I thought a big one was there so I was disappointed to miss out."Scoreboard
New Zealand 1st innings 375 (T. Latham 105, D.Mitchell 73, B. Watling 55, R. Taylor 53; Broad 4-73, Woakes 3-83)
England 1st innings (overnight 39-2)
R. Burns run out (Raval/Watling) 101
D. Sibley lbw Southee 4
J. Denly c Watling b Henry 4
J. Root not out 114
B. Stokes c Taylor b Southee 26
Z. Crawley c Watling b Wagner 1
O. Pope not out 4
Extras: (lb14, nb1) 15
Total: (5 wkts; 99.4 overs) 269
Fall of wickets: 1-11, 2-24, 3-201, 4-245, 5-262
To bat: S. Curran, C. Woakes, J. Archer, S. Broad
Bowling: Southee 26-3-63-2, Henry 21.4-5-56-1, Wagner 23-3-76-1, Mitchell 12-4-28-0 (1nb), Santner 17-4-32-0
Toss: England
Series: New Zealand lead 1-0
Umpires: Kumar Dharmasena (SRI), Paul Wilson (AUS)
TV Umpire: Bruce Oxenford (AUS)
Match Referee: Javagal Srinath (IND)
Karn Sharma and Swapnil Singh bag four key wickets to secure a 35-run victory in Hyderabad
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