Root, even while presiding over a run of just one win from 17 Tests prior to this series that prompted his resignation as captain, kept making runs -- in 2021 he scored 1,708 in Tests at a superb average of 61.
Such was New Zealand's desperation to dismiss Root they wasted two of their three reviews this innings off successive Tim Southee deliveries in near-identical attempts to get clearly correct not out lbw decisions overturned when the star batsman was on one.
Root delighted his loyal fans with an outrageous reverse-ramp six off Neil Wagner, with the left-arm quick hit for three fours in consecutive deliveries by the increasingly assertive Pope.
And with Headingley bathed in sunshine, the last over of the day saw Root complete a 78-ball fifty with a legside boundary off Bracewell.
Selected for just his second Test ahead of Ajaz Patel, a frontline spinner, Bracewell had expensive stumps figures of 1-70 in 11 overs.
Stokes' confidence in Leach
Earlier, New Zealand's Daryl Mitchell and Tom Blundell had frustrated England yet again with their fourth century stand of the series before Matthew Potts sparked a collapse.
Leach had already secured a place in Headingley history with a memorable one not out in a dramatic one-wicket Ashes Test win over Australia in 2019.
But this week he 31-year-old has excelled in his main role of left-arm spinner by taking 10-166 in his 25th Test, with the Somerset favourite following a first-innings haul of 5-100 with an even better 5-66 on Sunday.
Those figures were a testament to both his skill and the faith shown in Leach by new England captain Ben Stokes.
"It was very special here at Headingley, I had good memories from 2019 and first game back here and I enjoyed it," Leach told Sky Sports.
"Stokesy's confidence in his decisions and in us is like nothing I have ever experienced before."
Leach polished off the tail after Potts, in his debut Test series, had made a key breakthrough by removing the in-form Mitchell lbw for 56 to end a sixth-wicket stand of 113.
Mitchell, who only played in the series opener at Lord's after Henry Nicholls was sidelined, finished a campaign where he scored three hundreds with a tally of 538 runs -- the most by any overseas batsman in a series of three Tests or fewer in England
When the 31-year-old was out, the Black Caps were still well-placed at 274-6, a lead of 243. But they were all out for 326.
Leach lured Bracewell into hoisting a catch to deep midwicket before deceiving Southee with a quicker arm ball.
Wagner then fell in unusual fashion when replacement wicketkeeper Sam Billings, who only took the field Sunday as a Covid-19 replacement for Ben Foakes, grabbed an edge off Leach that had lodged between his legs.
When Leach bowled Boult to end the innings, Blundell was left stranded shy of what would have been his second century of the series on 88 not out.
"We've just got to fight," Blundell told reporters. "We've got to come out first thing tomorrow (Monday), put a couple of wickets on the score and you never know."