Both teams have a point apiece in the one-day worldwide tournament after they were each well beaten by England, while their respective matches with Australia ended in rain-induced no results.
However, it was a break-neck innings from wicketkeeper-batsman Jos Buttler which pushed the total to 310.
However, the tourists' chase got off to a terrible start with Luke Ronchi dismissed for a golden duck, and though Kane Williamson hit an impressive 87, they were bowled all out for 223 with just over five overs remaining.
Martin Guptill (27) and Williamson dug in before the former edged an intended drive off all-rounder Stokes to Root at a wide slip.
It set the tone for England to grab the initiative, with Liam Plunkett the pick of the bowlers as he took 4-55 in a commanding triumph for his side.
But he said Eoin Morgan's men were now a much improved one-day outfit.
It was the end of Williamson's 98-ball innings featuring eight fours. The ball was going out of the entire ground until it hit the camera gantry.
Adil Rashid was restored to the team here in place of the injured Chris Woakes and the leg-spinner was impressive, taking two for 47 from his 10 overs.
Although it is not a new trend for players to pay their respects in the aftermath of a tragic event, this is perhaps the first time that a match was halted in between so that players can observe a minute's silence.
The No.3 accumulated a solid fifty from 66 balls without ever dominating and was undone by a snorter from Mark Wood which bounced off his gloves to the keeper.
Earlier, Hales scored his second 50 of the tournament but was bowled by Milne for 56 off 62, right after hitting the same bowler for six over longoff.
Facing Trent Boult in the 46 over of the innings, Buttler moved to the offside and ramped the ball over his left shoulder.
Plunkett joined in by pulling Milne for a six that brought up England's 300 but the steady fall of wickets kept the Blackcaps in the game.