Root, who came in at 67 for three after England lost two wickets in two balls on that score, was 61 not out on his Headingley home ground and fellow Yorkshireman batsman Jonny Bairstow 13 not out.
It was another composed display by the 22-year-old Root, now in his sixth Test but yet to make a hundred, following his 71 in the second innings of England's 170-run win in the first of this two-match series at Lord's last week.
Afterwards, the experienced Bell clipped left-arm quick Trent Boult for four while Root cut and forced Tim Southee, who took 10 wickets at Lord's, for two boundaries.
Southee thought he'd reduced England to 100 for four when Bell was given out lbw for 12 by Marais Erasmus.
Bell, though, reviewed the South African umpire's decision and, with technology indicating the ball would have bounced over the stumps, he was reprieved.
New Zealand's four-man seam attack -- spinner Bruce Martin suffered a tour-ending calf injury at Lord's while Daniel Vettori was declared unfit Thursday -- kept England's fourth-wicket duo under pressure.
And when left-arm seamer Neil Wagner gave Root width, he was cut behind square for another boundary.
However, part-time off-spinner Kane Williamson lived up to his reputation as a partnership breaker when he had Bell, carelessly trying to run the ball down to third man caught behind by New Zealand captain Brendon McCullum for 30.
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