Buttler (129) scored the second-fastest ODI hundred by an Englishman ??? off 66 balls ??? and Root (104) the fourth ??? off 71 balls ??? to help their country post 408-9 during a spellbinding innings at Edgbaston.
Adil Rashid (69) and Eoin Morgan (50) ??? the??former during a record-breaking 177-run stand with Buttler for the seventh wicket ??? also crunched half-centuries, with Trent Boult (4-55) the only Black Caps bowler to avoid a drubbing.
Boult struck with the first ball of the innings, having Jason Roy (0) pouched at backward point after New Zealand won the toss, but Alex Hales (20 from 20) and Root then smoked a quick-fire fifty partnership off 43 deliveries.
Hales??? departure early in the eighth over ??? the Nottinghamshire top-edging a Boult bouncer to backward square-leg ??? didn???t disrupt the hosts??? flow, with skipper Morgan equally aggressive.
Root was the star man, cutting, pulling and driving gloriously all over the wicket while notching 13 fours and two sixes, though Morgan creamed three maximums en route to passing fifty in ODIs for the first time since clubbing a ton against Australia in January.
The pair put on 121 for the third wicket in 96 balls before Morgan was trapped lbw by Mitchell McClenaghan in the 23rd over, an over prior to Root pushing Matt Henry inside mid-on to secure his fifth one-day international century.
Root???s knock came to a close when he flicked Boult behind to Luke Ronchi and when Ben Stokes (10) chopped the same bowler on and Sam Billings ??? on his maiden England appearance ??? was caught lbw by fellow debutant Mitchell Santner, England had lost four wickets for 31 runs.
However, Buttler – whose 61-ball effort against Sri Lanka remains the quickest ODI century by an Englishman – and Rashid teamed up to excellent effect, posting the highest seventh-wicket partnership in one-day internationals.
Buttler, who was dropped by Ross Taylor in the deep when on 90, bashed 13 fours and five sixes during before slapping to square-leg in the 48th over as England beat their previous best ODI total of 391, set against Bangladesh at Trent Bridge in 2005.
Liam Plunkett (13no from three) then smashed a six off Grant Elliott in the last over to deny the bowler a hat-trick????? the seamer had snared Chris Jordan (2)??and Rashid in successive deliveries????? and ensure 400 was totalled in an ODI in England for the first time.