England's score was their highest in all one-day internationals, surpassing the 391 four they made against Bangladesh at Trent Bridge in 2005 -- the previous highest in any ODI in England.
It owed much to a stand of 177 between Buttler and Adil Rashid (69) -- a record for the seventh wicket in all ODI cricket, topping the 130 put on by Zimbabwe's Andy Flower and Heath Streak against England in Harare in 2001.
That partnership meant the huge score England had threatened while Joe Root, who made 104, and captain Eoin Morgan (50) were compiling a third-wicket stand of 12, was achieved despite the loss of four wickets for 31 runs in the middle of their innings.
But the left-arm paceman had completed his spell when England's seventh-wicket pair launched their assault against the remainder of the World Cup finalists' attack.
This fixture, the first of a five-match series, marked the start of what England hoped would be a new era of one-day international cricket after their embarrassing first-round exit at this year's World Cup, which included an eight-wicket thrashing by New Zealand in Wellington in February.
But it started with a whimper when, after New Zealand captain Brendon McCullum won the toss, the first ball of the innings saw Jason Roy caught by Martin Guptill at backward point off Boult.
Root had two moments of good fortune. He went to fifty when an outside edge off left-arm quick Mitchell McClenaghan flew between wicket-keeper Luke Ronchi and slip Ross Taylor, with neither man going for the chance.
And after sweeping off-spinner Nathan McCullum for six, the next ball, on 61, saw Taylor drop a difficult, low, one-handed catch as the ball went for four.
He pressed on to an excellent hundred -- his fifth in 51 ODI innings -- off 71 balls, including 12 fours and two sixes.
But he fell soon afterwards, caught behind off Boult, to spark a slump.
Buttler, whose maiden ODI century against Sri Lanka last year came in an England record 61 balls, took 66 to reach the landmark at Edgbaston.
The 24-year-old went to three figures in style when he cover-drove McClenagan for his 11th four.
Meanwhile New Zealand's fielding was below its usual high standard with Brendon McCullum dropping Rashid in the deep when the leg-spinner had made 46.
Buttler's superb innings ended when he holed out off Henry, having faced just 77 balls including 13 fours and five sixes.
Grant Elliott took two wickets in two balls in the last over, Rashid falling for his ODI best score made off just 50 balls, including seven fours and two sixes.