Match scores (Derby)
England won by 75 runs
England: 284-9 (50/50 overs. Sciver 129, Beaumont 93; Kerr 4-51, Kasperek 2-49)
New Zealand: 209 (46.4/50 overs. Bates 44, Perkins 43*, Satterthwaite 35; Hartley 3-44, Shrubsole 2-19, Gunn 2-32)
Match report
England qualified for the Women's World Cup semi-finals with a 75-run win over New Zealand at Derby, where Natalie Sciver hit a second century of the tournament.
Sciver's 129, and 93 from fourth-wicket partner Tammy Beaumont, helped England recover from 52 for three to set a victory target of 285.
Once New Zealand captain Suzie Bates was out for 44 and Amy Satterthwaite for 35, the lower order never looked like salvaging a positive result despite a determined unbeaten 43 from Katie Perkins as three wickets from Alex Hartley helped seal victory.
England move top of the table above Australia on run-rate ahead of their final group match against the West Indies in Bristol on Saturday.
New Zealand must now beat India, also at Derby, to join them in the last four.
England captain Heather Knight said on Sky Sports: "We were really under pressure and it was hard work, so I am really pleased how the girls went about it to secure that semi-final spot.
"We have got one (group) game to go now on Saturday, so we would love to continue the winning habit at Bristol and will try to play the best team we can."
England, who had beaten Australia by three runs in their last match, won the toss and elected to bat.
Opener Lauren Winfield was soon out for 11, well caught at backward point by Satterthwaite who was making her 100th New Zealand one-day appearance.
Wicketkeeper Sarah Taylor and Knight made just eight apiece to leave England struggling but Beaumont and Sciver, who had scored a century against Pakistan, steadied the innings.
Their stand of 170 included Sciver clipping a leg-stump yorker deftly through her legs for two - a shot quickly christened the "Natmeg" - as the pair lifted England to 222 before Beaumont, who had earlier seen a delivery from Leigh Kasperek clip leg stump without dislodging the bail, holed out to Lea Tahuhu at mid-off from the bowling of 16-year-old leg-spinner Amelia Kerr.
Beaumont's contribution ended from 102 balls, which included 10 fours and a six, before Sciver brought up her century off 92 deliveries. She finally fell to Kerr in the 47th over and was given a standing ovation by the County Ground crowd.
From 269 for six, England quickly lost Jenny Gunn, with Katherine Brunt, marking her century of one-day international caps, out for nine, again to Kerr who finished with four for 51 after bowling Anya Shrubsole for a duck.
England then made an early breakthrough, Rachel Priest bowled by Shrubsole for 12, and restricted New Zealand to just 36 from the first 10 overs before Satterthwaite and Bates pushed things on.
Following the drinks break, Bates was stumped off left-arm spinner Hartley for 44, with Satterthwaite caught and bowled by Laura Marsh to leave New Zealand at 99 for three and the momentum firmly back with England.
When Perkins ran out Kerr without the youngster facing a ball, New Zealand were on the brink at 170 for eight and England's victory was soon wrapped up when Holly Huddleston was lbw for nought to Hartley, who finished three for 44.