The points were short and sharp for most of the battle and followed the same pattern in both sets, with the two swapping breaks early on and then 12th seed Zheng snaring the extra break in the seventh game both times.
"It feels unbelievable," Zheng said on court after the match.
"I'm super excited to have such a great performance today and get into the final. My opponent played unbelievable tennis and has really good baseline strokes. It's tough to explain my feelings now."
Zheng, who has rained down more aces by far than any other woman at Melbourne Park in her journey to the final, is bidding to match her hero, Li Na, who won the Australian Open crown 10 years ago.
"We love her," Zheng said of Li, whom she said advised her earlier in the tournament to not think too much and "just go for it."
But after beating a string of lower-ranked players to reach the final, she will now face a formidable opponent in Belarusian second-seed Sabalenka, who has not lost a set in the past two weeks.
"I'm sure the final will be really competitive because I think Sabalenka, she's one of the most big hitters right now in the tour," Zheng told reporters.
She and Sabalenka practised together ahead of the tournament, and the Belarusian said she expected a "great battle" with Zheng in the final.
In her semi-final, Zheng kept up the pressure on Yastremska in the first set, blasting cross-court winners off both wings and left the Ukrainian clutching her abdomen in pain.
After taking a medical timeout off court, Yastremska returned to court with Zheng holding in the next game.
The Ukrainian extended the set by winning the following game with a clever drop shot but piled on the errors to hand Zheng the first set.
Zheng started off stronger in the second set, holding her first service game to love and then snatching an early break after a string of errors from Yastremska, but the Ukrainian broke straight back.
Zheng broke again in the seventh game, helped by a double fault from Yastremska and a shanked shot that flew long.
Yastremska bravely held her serve, with Zheng fluffing an easy smash, but the Chinese player then came back to clinch the match with an unreturnable serve.
"She played great today, but I think if I felt a little bit more fresh the win would be on my side," Yastremska told reporters.
