In doing so, the Belarussian became the only qualifier ever to reach the tournament’s final.
Sevastova looked far from good form, though both competitors dropped a game in the first set, and Sasnovich managed to edge her opponent in the tie-breaker.
Svitolina to take on reigning champ Pliskova in Brisbane semis
In the second set, Sevastova squandered two break points in the sixth game. After Sasnovich broke in the ninth, Latvian Sevastova had nothing left in her Arsenal and Sasnovich won the second set 6-4.
Speaking after the match, Sasnovich admitted: "I was very close to Anastasija. We play same level, but I was a little bit like her today. I used all my chances today as well.
"I had a good serve, good play from the baseline. I'm happy with my win today."
In Friday's second semi-final match, Elina Svitolina triumphed after beating Karolina Pliskova 7-5, 7-5 after she was beaten in the semi-finals of the same tournament last year by the Czech.
Sasnovich and Svitolina will meet in the final on Saturday.
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Dominant Svitolina cruises into Brisbane quarter-finals