Yesterday's success means England will return to the Welsh capital as Group A winners for a last four clash against the as yet unknown Group B runners-up on June 14, in an event featuring the world's leading eight one-day international teams.
England looked to have fallen short of a par score despite making 310 all out after Joe Root (64), Alex Hales (56) and Ben Stokes (48) were all dismissed when well set before Jos Buttler's unbeaten 61 boosted the total.
Williamson's exit sparked a collapse that saw New Zealand lose their last eight wickets for 65 runs on the way to a total of 223 all out.
Liam Plunkett took four for 55, with his fellow paceman Jake Ball named man-of-the-match after striking early to dismiss Luke Ronchi for a duck on his way to fine figures of two for 31 in eight overs.
Meanwhile, leg-spinner Adil Rashid justified his recall in place of injured all-rounder Chris Woakes with a 10-over return of two for 47.
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Morgan feared England didn't have enough runs to play with after being sent into bat by Williamson.
"I thought we were probably 10 or 15 below par -- given that 320 is probably a par score regardless of the game we're playing in these days," said Morgan after England had still passed 300 in half of their 46 ODIs since a humiliating first-round exit at the 2015 World Cup.
Wood produced a superb delivery that Williamson, seemingly on course for a second successive century after his hundred in the Blackcaps' rain-ruined no result opener against Australia, could only glove to diving wicket-keeper Buttler.
"I thought they did an outstanding job. They were truly the highlight of the day.
"Our batting performance was probably par or below par -- so pretty average."
- 'Unique' Wood -
=================
Williamson, reflecting on the delivery from Wood that ended the innings said the Durham quick, fit following a persistent ankle injury, was a tough man to face.
"He's a very good bowler, unique in the fact that he bowls at such good pace off maybe a five to 10-metre run-up -- which you don't see too much around the world," said Williamson.
Defeat was made worse for Williamson when the International Cricket Council fined him 40 percent and his players 20 percent of their match fees for a slow over-rate during England's innings.
Morgan, meanwhile, knows his side will top the group regardless of the result of their final pool fixture against Australia, on Saturday, where a win over their Ashes rivals for the second time in successive Champions Trophy editions at Edgbaston would likely eliminate their oldest foes.
"I think if we're truly going to be contenders for this tournament, we need to beat the best teams -- and Australia are one of the best teams," he said.
"They always are going into a white-ball tournament. They seem to produce limited-overs cricketers at will," the former Ireland international added.
"So to go into a game like that with no other attitude than winning is very important to us.
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