At stumps, England -- who had been 30 for four when Stokes came in -- were 354 for seven after New Zealand captain Brendon McCullum won the toss and fielded.
Root (98) and Stokes (92) had put on 161 for the fifth wicket.
Jos Buttler (67) and Moeen Ali (49 not out) then added 103 before the wicket-keeper was lbw to Trent Boult off the last ball of the day.
They were also up against a reinvigorated New Zealand side fresh from a run to the World Cup final that saw England humiliated along the way.
And when England lost those four early wickets, it looked like their woes were about to multiply.
Yet it was two of England's 'young guns', the 24-year-old Root and the 23-year-old Stokes who turned the tide in the first of this two-match series.
Earlier, New Zealand were quickly among the wickets even though their three frontline bowlers -- including Test debutant Matt Henry -- plus McCullum himself, had only arrived in England just days before after stints in the Indian Premier League.
Instead debutant England opener Adam Lyth, selected after Jonathan Trott retired following a run of low scores during the drawn series in the West Indies, was caught behind off Tim Southee for seven.
The 100th Test between England and New Zealand then saw the hosts lose three wickets for five runs in 15 balls.
Boult had Gary Ballance caught at third slip for one before England captain Alastair Cook (16) fell when, beaten for pace by 23-year-old Canterbury quick Henry, he top-edged an attempted hook through to wicket-keeper BJ Watling.
At lunch, England were 113 for four with Root 49 not out and left-hander Stokes unbeaten on 36.
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