Earlier, Jos Buttler´s quickfire unbeaten 61 helped take England to a total of 310 all out after being sent in to bat in overcast conditions by New Zealand captain Williamson.
Jake Ball, a disappointment in England's opening day win over Bangladesh, set the tone for England when he removed the unsafe Luke Ronchi in the first over of New Zealand's response.
Victory saw England into the last four of a tournament featuring the world's top eight one-day global sides after an eight-wicket defeat of Bangladesh at the Oval last week, regardless of the result of their last Group A match against arch-rivals Australia at Edgbaston on Saturday.
"Our batting performance was probably par or below par".
England will finish group winners whatever the outcome of their final match against Australia at Edgbaston on Saturday - when a win over their Ashes rivals, for the second time in successive editions of this tournament, is very likely to eliminate their oldest adversaries.
"It feels good to be in the semis but we are not satisfied", said Morgan.
Williamson, who escaped a ban for his side's slow over rate but was docked 40% of his match fee to go with 20% for his players, had few complaints over the result and admitted England's attack simply made better use of the two-paced pitch.
Morgan also praised leg-spinner Adil Rashid, who had figures of 2/47 from his 10 overs.
"We'll have a very serious attitude", said Morgan.
He said: "I certainly think [we have alighted on our best team]".
"Their batsmanship is ridiculously unbelievable, they know the game inside out and it's a master class when they get going". "They seem to produce limited-overs cricketers at will", the former Ireland worldwide added.
"I thought we looked like we were getting about 340 at stages, but fell away towards the end, which is disappointing. It's a must-win game and as a bowling unit we definitely need to take wickets".
But Buttler ensured England get past the psychological 300-run mark with a crucial 49-run stand off just 30 balls for the eighth wicket with Liam Plunkett (15).
Trump's lawyer denies he's being investigated
Well known in the Manhattan business circles that Trump inhabits, Kasowitz has a reputation as a bare-knuckles court brawler. It seems to me largely semantics, but the is-he-or-isn't-he argument stems from the latest push by the White House.
No offer received for Ronaldo, says Real boss
The current Ballon d'Or holder, at 32-years-old, has made public that he is not content at the Bernabeu and could seek to depart. He is now with the Portugal side at the Confederations Cup and his future plans will likely become clearer after its conclusion.