She came into the match an overwhelming underdog having never beaten her opponent in five previous attempts, but left shedding tears of joy after masterminding a 7-5 1-6 6-3 victory.
The petite, yet nimble-footed, Italian had been expected to struggle with Stosur's high, kicking serve and heavy topspin groundstrokes, but contrived to out-think and outmanoeuvre the Australian.
"I have no words, it is incredible," a weepy Errani, who collapsed on to her back in her moment of victory, said on court afterwards.
Stosur had fallen into the 21st seed's intelligently contrived plan to force her opponent out of her comfort zone and nullify her principle weapons.
She stepped inside the baseline to take the Stosur serve early and looked to keep the Australian on the back foot with some deep, penetrating groundstrokes.
"She is a smart player," was Stosur's simple assessment after seeing everything she could throw at her opponent come back at with interest.
Stosur, the U.S. Open champion, was the experienced player, having been at this stage of the competition twice before.
The sixth seed had also bulldozed her way to the last four without dropping a set.
She had her moments. She was quicker out of the blocks after heavy rain suspended the start of play, taking a 2-0 lead, but Errani claimed the first set by utilising clever angles that crowbarred her opponent out of position.
The Australian struck back with a dominant display of power hitting in the second set which exposed Errani's lack of a truly penetrating shot of her own.
But just when the momentum had switched in her favour, she froze on the big stage and as she tightened up Errani capitalised on a string of unforced errors to wrap up the match.
"Maybe she had more pressure," a delighted Errani told reporters. Maybe I was more focused on the more important moments."
Errani will play Maria Sharapova in the final on Saturday after the second seed swept aside Petra Kvitova.
Whether she wins or loses, Errani, who has beaten former champions Ana Ivanovic and Svetlana Kuznetsova en route to the weekend showpiece, will move into the top 10 when the rankings are next published.
"I don't feel like top 10, so it's a strange sensation," a modest Errani said.
"Maybe my problem always was that I couldn't believe enough to win against the strong players.
"But now I beat three in a row. I'm in the final in a grand slam, so I have to try to think a bit differently."