The defending champion appeared to pick up injuries to her left knee and then to her ribs but ran out a relatively comfortable 6-1 6-4 winner against the American 19-year-old.
Azarenka will have two days to recover before the final against Li, who demolished Maria Sharapova earlier in the day.
The Belarusian, 23, looked flustered early in the second set and her frustration level increased when the 29th ranked Stephens saved five match points with Azarenka serving at 5-3.
However, the top seed seized the opportunity on Stephens's next service game to close out the match.
"I almost did the choke of the year right now," Azarenka said courtside. "At 5-3 having so many chances, couldn't close it out but I'm glad I could close it out. Nerves got into me for sure.”
Hailed as the future of American women's tennis, Stephens caused the biggest upset of the tournament less than 24 hours earlier by beating 15-times grand slam winner Serena Williams.
The confident teenager had spoken about dealing with the big occasion by believing she did not have anything to lose against Azarenka but she began nervously and dropped her first service game.
Azarenka exploited the teen's early wobbles and blasted away on her own service game to hold to love and take a 2-0 lead.
She broke Stephens for the third time to seal the set in 33 minutes with a delightful backhand lob that the 19-year-old barely even bothered to turn and chase.
The world number one continued to work Stephens around the court and took a 2-0 lead in the second set, but while serving in the next game she seemed to jar her left knee and ankle while chasing a ball on her backhand.
Azarenka hopped, and gingerly placed her foot back down on the ground, then wandered to the back of the court where she leaned against the advertising hoarding.
Stephens sensed her opportunity and broke Azarenka for the first time, then got the set back on serve as the pair slugged it out from the baseline.
Azarenka, who had troubles keeping her emotions in check earlier in her career, gritted her teeth and broke Stephens to love to take a 4-2 lead but then struggled to hold her own serve and slammed a ball into the hoardings in frustration.
After blowing chances to seal the match at 5-3 Azarenka received treatment courtside at the changeover, when medical staff looked to be checking her ribs, then she asked for a medical timeout.
The delay settled Azarenka and she sealed her place in the final on Stephens's next service game, and sixth match point, when the American's backhand sailed over the baseline.
"I think Li Na is playing (some) of her best tennis right now ... it's going to be a tough match," Azarenka said.
"It's going to be the first time we meet in a final ... it's a tremendous achievement and I'm really glad I pulled through."
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