England's Wyatt, Ecclestone set up World Cup final with Australia
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Wyatt's outstanding 129, aided by five dropped catches and supported by Sophia Dunkley's 60, saw England post an imposing 293 for eight off their 50 overs at Hagley Oval in Christchurch.
Sophie Ecclestone then produced the best bowling figures of the tournament with six for 36 as South Africa folded for 156 in 38 overs.
After being on the brink of elimination after losing their first three matches, the defending champions have since won five in a row and will now face unbeaten Australia in Sunday's final, also at Hagley Oval.
"That was a complete performance from us today, what we've been searching for," said captain Heather Knight who rated her side as "underdogs" against Australia.
"But we're all equal on the morning of the game and what a story is written for us if we can do it."
Player of the match Wyatt, who scored only 12 fours in her 129 off 125 deliveries -- the third highest score of the tournament -- said it was a difficult ground for batting.
"I tried to capitalise on the width provided by their bowlers. The boundaries were pretty big," she said.
"It was a weird wicket. We just said run well between the wickets and just be positive."
It was the second consecutive World Cup that England have beaten the Proteas in the semi-finals and continued South Africa's last-four hoodoo with no men's or women's team having reached an ODI or Twenty20 World Cup final.
They started well when they won the toss and reduced England to 77 for three but opener Wyatt was standing firm.
Wyatt was eventually out off the bowling of Masabata Klaas, caught by Lizelle Lee who had dropped the first chance offered by Wyatt when she was on 22.
Dunkley made her 60 off 72 deliveries and the innings was finished in style by Ecclestone's quickfire 24 off 11 balls.
The all-rounder smacked three consecutive fours in the final over before being bowled by Shabnim Ismail, who finished with the best South African figures of three for 46.
South Africa's run chase started disastrously when the tournament's highest run-scorer Laura Wolvaardt was out without scoring in the second over and big-hitting opening partner Lee followed in the fourth over for two.
From eight for two, South Africa were in further trouble when captain Sune Luus went for 21, leaving them 44 for three in the 12th over and well behind the required run rate.
At the halfway stage they were 95 for four with the rising required run rate of 7.96 proving beyond them as the tournament's leading wicket-taker Ecclestone ran through the tail to take England to their sixth appearance in a World Cup final.