Buttler reached his century in 66 balls, the second fastest by an England batsman; the man-of-the-match failed to displace his own 61-ball effort against Sri Lanka last May.
His strokes, including five sixes and 13 fours fanned the ground. As the New Zealand bowlers tried harder to distract him, Buttler chased them with more willow. He was matched by Joe Root who made 104 from 78 balls.
"On a good wicket it's hard to bowl to those batsmen when they're 'in'," Trent Boult said, having been the best of New Zealand's bowlers with four for 55 after completing his allotment by the 33rd over. "[Jos is] dangerous, as good as anyone on their day to take apart a bowling unit. He's hard to shut down, is running into hot form and is a significant person to scout.
"Joe also batted well and the partnerships flowed from there. We did well to pull them back to 202-6 with the hope of bowling them out for under 300, but there was another key partnership. There seemed a lot of room with only four fielders out, and they hit the gaps brilliantly. We quickly found out it was a good surface."
"Those were special performances," captain Brendon McCullum said of Root and Buttler. "To post 400 in any game is outstanding... they blew us off the park.
"Sometimes you've got to admit when you get it wrong at the toss. The way the ball started holding up in the second innings probably suggested we got it wrong. We've got some work to do."
"It was as close to the perfect performance in a one-day game," England captain Morgan said.
"For a long time, we've talked about playing a different and aggressive brand of cricket. Today we've produced it."