Root scored 54 as England reached 352-9 declared in their second innings and challenged New Zealand to score 382 to win.
The clouds only darkened from there, much to the frustration of the tourists, who still need 10 wickets to square the series 1-1.
It was spinner Ish Sodhi and the third seamer Neil Wagner who took the spotlight instead, batting obdurately through the last 31 overs in a partnership broken only when the latter was dismissed with the last ball of the match.
From there, England were chasing eight further wickets for victory while New Zealand battled to hang on with 83 from opener Tom Latham, a 57-run standby de Grandhomme (45) and Sodhi, and then Sodhi and Wagner's stubbornness.
Wagner was out caught at silly point off England captain Joe Root, after a DRS review and the umpires then ended the match due to the poor light.
If New Zealand draw or win the Test it will see them triumph in a series against England for only the fourth time in 36 attempts.
Throughout the final session, England had believed they were in a race against the setting sun, with the vagaries of the South Island's autumnal weather likely to force a stoppage for bad light at any moment.
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"You want to play in big series and we've had the opportunity to do that this winter", Root said in the on-pitch presentation ceremony at Hagley Oval after England fell two wickets short of victory. "They started bowling bumpers around the wicket and I found them quite hard to pick up so there were tough periods there but once we go through that I think it was a pretty true wicket".
Sodhi remained undefeated on 56 off 168 balls, which included nine boundaries, as New Zealand finished on 256/8.
Broad's first ball strayed down the leg side and Jeet Raval, resuming at 17 with New Zealand 42 for none, steered it to Mark Stoneman at midwicket.
New Zealand have now beaten England four times in test series, most recently in England in 1999.
They were forced to do so the hard way - with fielders camped around the bat for the entirety of the final session, and having endured a stunningly awful start to the day's play, when two wickets fell to Stuart Broad's first two deliveries, including their likeliest final-day field marshall, Kane Williamson, for a first-ball duck.
Ross Taylor avoided the hat-trick, was dropped on six by James Vince and progressed to 13 when he saw Leach place Alastair Cook at short backward leg and promptly chipped the ball straight to him. The opener grafted 282 minutes over 83; Watling hung about nearly an hour and a half, and de Grandhomme 2h 17min until, just when he looked like carrying New Zealand to safety, played a daft hook to be caught at fine leg.
"I thought this was a great advert for Test cricket, these five days", he said.