Set 135 to win, South Africa reached their target with 16 balls to spare, with Bosch, who struck eight fours and a six in her 48-ball innings, sharing a match-winning partnership of 96 with skipper Laura Wolvaardt (42).
In Sunday's final, which will be the first not to feature one of Australia or England, the South Africans will face either West Indies or New Zealand who meet in the second semi-final on Friday.
Australia, who have won six of the previous eight editions, had been the odds-on favourites to win a seventh title in the United Arab Emirates.
However, they had no answer to South Africa for whom this marked a measure of revenge for defeat by Australia in last year's final in Cape Town.
"I think this is one of the best wins of my cricketing career for sure. A couple of other girls have said it as well," said Wolvaardt.
"I think that was such an amazing chase. The bowlers are excellent. It's been a good year for us. I think it's been a real collective group effort."
Put into bat, Australia, who were again without their injured captain Alyssa Healy, struggled from the start with the normally fluent Beth Mooney top-scoring with a grafting 44 that included just two fours.
Healy's stand-in Tahlia McGrath made 27 and Ellyse Perry 31 but the run rate only got moving once Phoebe Litchfield came in to club a rapid 15 from nine balls.
The South Africans made a brisk start with Tazmin Brits hitting a six and a four before being bowled by Annabel Sutherland for 15.
That brought in Bosch who had had a mediocre tournament until Thursday with a highest score of 25 against Bangladesh.
She was quickly into her stride, using the slog sweep to great effect as she knocked all of the Australian bowlers apart from Sutherland off their rhythm.
She duly posted her third fifty in T20I cricket, going on to make her highest total in the format and the top score in this tournament.
"It was quite tough out there but I'm really glad we could get over the line and that I could finally contribute with some runs," said Bosch who was named Player of the Match.
"I can't really describe it but we knew we were capable of it and we had a pretty good tournament so far coming into this game and we were quite confident."
Wolvaardt, who is now the tournament's highest run-scorer with 190, fell just short of the finish with Bosch sealing South Africa's stunning win by smashing Megan Schutt through midwicket.
"It's going to be pretty hard to take," said McGrath.
"We just didn't really show up tonight. You can't afford to do that in tournaments like this. Full credit to South Africa. They outplayed us tonight."
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