England 305 for 8 (Bairstow 106, Roy 60, Neesham 2-41) beat New Zealand 186 (Latham 57, Taylor 28, Wood 3-34) by 119 runs
Chester-le-Street: England surged into their first World Cup semi-final since 1992 with a comprehensive 119-run defeat of New Zealand at Chester-le-Street on Wednesday.
The hosts are set to finish third in the group and will meet India or Australia at Edgbaston next Thursday for a place in the final.
Needing to defeat the Black Caps to be sure of progressing, England were led by Jonny Bairstow's dominant hundred, his second century in the space of four days.
Though they were checked as the New Zealand bowling improved, the England total of 305-8 seemed imposing on a pitch that gradually got harder to bat on.
And they were boosted by the run outs of both Kane Williamson and Ross Taylor - Williamson unluckily undone when backing-up - that left New Zealand 69-4.
From there, the Black Caps sucked the life from the spectacle with a limp attempt to defend their net run-rate, eventually being bowled out for 186 with Mark Wood taking 3-34 on his home ground.
Williamson's men have now suffered three successive defeats and have slipped to fourth in the table.
They will be caught if Pakistan beat Bangladesh on Friday, though it would need an almost impossible swing in run-rate to deny them a place in the semis.
Back-to-back defeats by Sri Lanka and Australia left England on the brink of an unthinkable exit, but they have responded with impressive wins over India and New Zealand, two fellow members of the top four.
Whereas Sunday's victory at Edgbaston was played in front of a crowd ferocious in its support of the Indians, here they were willed on by a loyal following in the Durham sunshine.
Eoin Morgan once again had the benefit of winning an important toss. Not only did batting seem easier early in the day - though that could have been due to the excellence of Bairstow and Jason Roy - but their three losses have come when chasing.
With a score on the board, England, again fielding four frontline pace bowlers, were a constant threat with the ball and superb in the field.
Jos Buttler took a wonderful diving catch to remove Martin Guptill and Adil Rashid's bullet throw accounted for Taylor.
England began the World Cup as the top-ranked side and favourites. Now they are playing well enough to justify both tags they will be feared in the semis, especially if they bat first.
New Zealand won five of their first six games, only to find themselves stumbling into their semi-final at Old Trafford on Tuesday against whichever teams tops the group.
Disadvantaged by the toss and an injury to pace bowler Lockie Ferguson, they started poorly with the ball, especially Santner and the returning Tim Southee, who was punished by Bairstow.
As England ran hard, New Zealand's fielding was sloppy, but the Black Caps gradually adjusted to the conditions and their improvement was led by the variations of medium-pacer Jimmy Neesham.
New Zealand's real problem is a reliance on the batting of Williamson - before today he had scored more than 30% of their runs in the tournament.
For that reason, the freakish way he was dismissed was a huge stoke of fortune for England and a mortal blow to the Kiwis.
As Taylor drove straight, bowler Wood got a finger-end to the ball before it crashed into the non-striker's stumps, with the desperate Williamson short of his ground.
In the next over, Taylor foolishly chanced Rashid's arm attempting a second and the contest was as good as over.