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The 22-year-old, roared on by a raucous home crowd that included Australian Prime Minister Scott Morrison and men's great Rod Laver, converted her fourth match point with an ace to seal the victory in two hours and 22 minutes.
The Czechs were without their two top players against a United States team who were the defending champions.
Katerina Siniakova and veteran Barbora Strycova powered the Czech Republic to the verge of another Fed Cup title in the final against defending champions the United States.
She is the first player to go through the season-ending tournament undefeated since Serena Williams in 2013.
Svitolina produced one of the best performances to overcome defending champion Wozniacki 5-7, 7-5, 6-3.
Karolina Pliskova became the first woman to advance to the last four of the tournament.
Caroline Wozniacki got her WTA Finals title defence back on track with a 7-5, 3-6, 6-2 victory over Petra Kvitova.
A land known for its generosity and hospitality, Jordan has always been open in receiving cultural as well as culinary influences from neighbours and guests.
Roger Federer handed Nick Kyrgios a 6-4, 6-1, 7-5 tennis masterclass by storming into the fourth round.
Williams, who won the Wimbledon title on her last two visits in 2015 and 2016, is now on an 18-match winning streak at the All England Club.