Victoria Azarenka, who will retain top spot on the rankings if she defends her title at Melbourne Park, needed six match points to defeat Stephens 6-1, 6-4 in 1hr 41min and move into Saturday's championship decider against Li.
"I almost did the choke of the year," Azarenka said, after losing five match points while serving at 5-3 in the second set. "So many chances. I felt a little bit overwhelmed. Nerves got to me, for sure."
In a dramatic ending, in scorching heat on Rod Laver Arena, Azarenka let slip five match points when she was serving for the match, before being broken for 5-4.
The Belarusian then called a medical timeout and left the court for 10 minutes to receive treatment for rib and knee complaints. When play resumed, Stephens was unable to hold serve and Azarenka made it into the final.
"It was important to overcome this little bit of struggle," Azarenka said.
"I couldn't lose. I just couldn't. That was why I was so upset. I couldn't breathe out there. It's a tremendous achievement and I'm so happy I pulled it through."
Stephens was coming off her upset of world number three Serena Williams on Wednesday, and much depended on how she handled her new-found superstar status.
Losing her opening service game was a portent of the hardships to come in a match that Azarenka completely dominated until her attack of nerves.
Azarenka slipped to a 2-0 lead. A strong service game from Stephens put her on the scoreboard but the American's groundstrokes were failing to hit the mark and the world number 25 made 16 unforced errors in the opening five games as Azarenka went two breaks ahead.
When Azarenka landed a perfect half-volley, backhand lob to take the first set in 33 minutes, Stephens had already racked up 19 unforced errors.
Azarenka jumped to another 2-0 lead to begin the second set. At 0-30 in the following game, she pulled up quickly, and appeared to be favouring her left knee.
She showed no discomfort in subsequent rallies. Stephens temporarily stemmed the flow of errors and broke Azarenka for the first time in the match, keeping herself in the hunt at 1-2.
Azarenka was limping, but she went on a run of nine straight points while taking a 4-2 lead. She appeared certain to romp through the final games but errors and double faults gave Stephens an unexpected reprieve.
Serving at 3-4, with the crowd behind her, Stephens missed a routine smash on the way to being broken for the sixth time in the match.
Azarenka then passed up five match points in her anxiety-riddled attempt to serve out the clash, and called for the trainer at the changeover.
She took a 10-minute medical timeout and left the court. When she returned, Stephens was serving to stay in the match but Azarenka snuck through on match point number six.
The 23-year-old Azarenka must defeat Li in the final to retain her number one ranking. Otherwise, America's Williams will take top spot.
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