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Wyatt, dropped five times by the wasteful South Africans, made 129 off 125 balls today to help England put an imposing 293 for eight on the board at Christchurch's Hagley Oval after South Africa won the toss and elected to field.
Seamer Anya Shrubsole, the hero of the 2017 World Cup final, pressed the advantage by removing both South Africa's openers cheaply before the world's top-ranked spinner Sophie Ecclestone took six wickets as South Africa were routed for 156.
Having started the tournament with three straight defeats, Heather Knight's England have rebounded with five wins.
Their victory over South Africa was their most complete performance of the tournament, with Sophia Dunkley chipping in 60 in a 116-run partnership for the fifth wicket.
The English may need to lift again to beat undefeated Australia, who are hot favourites after thrashing West Indies in the other semi-final and have a chip on their shoulder after being knocked out of the 2017 semi-finals.
Australia are unlikely to reproduce South Africa's ragged fielding display, which saw Wyatt dropped on 22, 36, 77, 116 and 117 before she was finally caught by a scrambling Lizelle Lee after hitting Masabata Klaas to short third man.
By that time, England were well on the way to setting South Africa a would-be world record chase.
The final will be held at Hagley Oval on Sunday from 1pm (NZ time).