On a wonderful batting surface for this Royal London Series opener, it was the hosts rather than World Cup finalists New Zealand who proved they had the necessary firepower with a national-record 408 for nine in a huge win.
As they kick-started the fresh approach under Eoin Morgan after their own miserable World Cup winter, England were chiefly indebted to Root (104) and Buttler (129), who dominated a world record seventh-wicket stand with Adil Rashid (69).
Then Rashid (four for 55) in particular did enough with the ball too for a career-best in both disciplines as the Kiwis predictably found the first 400-plus total in England’s 50-over history beyond their range.
Ross Taylor (57) got most back with the bat after his torrid day in the field, but not enough to stop England recording victory by their highest ever runs margin, with almost 19 overs unused.
Root’s 71-ball hundred was, for an hour or so, England’s third-quickest until Buttler, already the scorer of their fastest, made it a one-two with his latest century off 66.
England’s progress with their new spirit of adventure was sporadic but undeniably effective – in Root and Morgan’s third-wicket stand of 121 and then, after a mid-innings blip, Buttler and Rashid’s 177.
After being put in, the hosts overcame the loss of Jason Roy to the first ball of the match, his maiden ODI innings lasting the minimum when he speared a drive at Trent Boult (four for 55) to point.
Root and Alex Hales put on a quickfire 50 until the opener mis-pulled Boult high to short fine-leg.
Brendon McCullum’s attempt to unsettle his Indian Premier League pal Morgan (50) with an overloaded off-side field bore no fruit, and the Irishman was soon matching Root shot for shot.
That was no mean feat, with the Yorkshireman in brilliant form.
There was barely a false shot from Root, the exception his edge between wicketkeeper and slip off Mitchell McClenaghan to bring up his 50 with his seventh four.
Having escaped just one half-chance on 61 at wide long-on off when Taylor could not cling on diving one-handed to his right, he completed his fifth ODI century.
But McClenaghan pinned Morgan in front, working to leg, and two overs later Root was gone too, edging behind as he tried to stay on the attack against the returning Boult.
Ben Stokes’ departure defied conventional description, under-edging a pull down on to his leg and then stumps, and then Sam Billings was done in the air by his fellow debutant Mitchell Santner to go lbw.
But despite four wickets for 31 runs, Buttler and Rashid stuck to the plan with supreme skill and strength.
Buttler was dropped on 90 by a diving Taylor again at deep midwicket off Matt Henry and eventually mis-pulled McClenaghan after hitting 13 fours and five sixes, while Rashid passed his maiden international half-century.
New Zealand’s reply was mission improbable from the outset, all the more so when Steven Finn (four for 35) got rid of their biggest weapon – captain McCullum – bowling him as he went after a full-length delivery in the first over.
Martin Guptill edged England’s senior seamer behind and Kane Williamson became Rashid’s first victim when he was well-caught by Root running in from long-off.
A fourth-wicket stand of 66 between Taylor and Grant Elliott hinted briefly at a lasting chase.
But Billings interrupted it with a fine bit of fielding from third man to run out Elliott and Rashid, bowling mostly googlies, cashed in with three more wickets and even put himself on a hat-trick when Luke Ronchi missed an attempted slog-sweep first ball.
New Zealand then folded tamely, losing their last seven wickets for 38 runs.