Root, standing in as interim captain this week following Ben Stokes's curfew-breaking night out, followed Indian great Sachin Tendulkar as only the second player to reach 14,000 Test runs on Saturday's day four.
It was another remarkable achievement for the Yorkshireman, who was 75 not out at stumps, but with England needing a world record 463 it is one that seems destined to come in a losing cause.
After New Zealand were dismissed for 362 in their second innings, the hosts closed on 5-182, needing another 281 to win on a day-five pitch.
With Harry Brook's explosive 58 the next best score, it was impossible to ignore events 450km away in Chester-le-Street where the temporarily exiled Stokes was busy smashing 95 in Durham's Championship match against Northamptonshire.
No team has ever scored chased more than 418, with England's own record set at 378 four years ago. Root scored an unbeaten 142 on that occasion and even a repeat performance of those Edgbaston heroics probably won't be enough this time.
Merely reaching a fifth day appeared unlikely at one stage, with a flimsy start to the innings leaving them 3-40. Emilio Gay, Jacob Bethell and Ben Duckett all fell before the tea break, the latter to a horribly-executed hook shot, before a fourth-wicket stand of 97 between Root and Brook lifted home spirits.
Root played a studious role in the partnership while Brook launched a counter-attacking frenzy that brought him a 33-ball half-century including 10 fours and a six.
New Zealand's talented attack found a way to apply the brakes and restricted him to seven from the next 21 deliveries, before he squeezed Matt Henry to slip.
That left Root to see things through to stumps, with the absence of Brook's fireworks allowing the tourists to restore calm to proceedings.
There was only one serious scare in his composed 137-ball stay, given lbw on 44 but instantly reviewing the decision as DRS showed an inside edge.
England had earlier produced an efficient effort, Jofra Archer removing Henry Nicholls for 121, with just two added to his overnight score, before he also won his latest duel with first-innings centurion Glenn Phillips.
Matt Fisher picked up three soft wickets as Daryl Mitchell, Jamieson and Nathan Smith swung the bat with abandon and debutant Sonny Baker grabbed the last wicket to end a difficult spell.
