Set a colossal 463 to win after New Zealand were bowled out for 362, Root came to the crease two runs shy of the milestone only Indian great Sachin Tendulkar has reached and with England tottering on 13-2.
Interim skipper Root was still there at the end of the day on 75 not out, although at 182-5, England's chances of avoiding defeat still look slender.
New Zealand will require five wickets to level up the series and set up a decider at Trent Bridge next week, while England still need an improbable 281 runs for victory.
"We've just got to try and stay patient tomorrow, stay ruthless. Whether it comes quick or in the last over of the day, we've got to make sure we're there," New Zealand fast bowler Kyle Jamieson, who bagged three wickets for 37 from 14 impressive overs, said.
Root, captaining the side for a record-extending 65th time after Ben Stokes was left out after breaking a team curfew, was his usual cool presence as he kept New Zealand's pace attack at bay on a sultry afternoon in south London.
England opener Emilio Gay made a positive start, driving Matt Henry elegantly through the covers for a boundary, but in the next over, he flicked a ball from Kyle Jamieson off his pads straight to square leg, where Rachin Ravindra took the catch.
Four balls later, Jamieson trapped Jacob Bethell plumb lbw for a duck, completing a miserable match with the bat for England's number three.
Opener Ben Duckett then played an awful shot off a short ball from Will O'Rourke, dollying a catch to Henry at mid-wicket to fall for nine.
Root was then joined by Harry Brook, and the pair decided the best policy in such dire circumstances was to attack.
Brook thumped two boundaries in one over off Nathan Smith, and in the next over, Root hit three off O'Rourke.
The belligerent Brook brought up his 50 off his 33rd ball, guiding Jamieson to the third man boundary.
Root was spared an lbw dismissal by an inside edge, but Brook's thrilling charge was halted when he edged his first-innings tormentor Henry to Daryl Mitchell.
Jamieson was rewarded for his relentless line and length as he trapped James Rew lbw for 15 late in the day on review.
With the weather set fair, Root will need one of the greatest innings of his illustrious career if England are to pull off a record run chase on Sunday.
Earlier in the day, New Zealand centurion Henry Nicholls added only two runs to his overnight 119 as he edged a superb Jofra Archer delivery to Brook at second slip.
Archer has impressed on his return to the Test team after being rested for the first Test, and also picked up the wicket of Glenn Phillips as he ended with three for 62.
Matthew Fisher also took three wickets as New Zealand's last four wickets went down for 13 runs after lunch.