Williams struggled with a back injury and left the court for treatment towards the end of the second set.
However, she broke serve immediately after returning, although ultimately surrendered the set.
Stephens, who looked up to Williams as her idol growing up, lost to the second seed in Brisbane recently, but was lost for words when asked her reaction to winning.
"My God, I don't even know," she said. "Oh my goodness.
"I'm sure my grandparents are going to be freaking out because they'll be watching it on the computer."
She said she planned to enjoy her showdown with Azarenka for a place in the Open final.
"You've just got to go out and do your thing again," she said.
Williams looked headed for victory when she cruised through the opening set and led 2-1 in the second.
Stephens then manufactured two service breaks in succession, gave up another when Williams came back on court, but steadily held to take the set and level the match with a break at 7-5.
Azarenka defeated Kuznetsova 7-5 6-1 to her way into the semi-finals in one hour 47 minutes.
Azarenka said she was prepared for Kuznetsova's tricky game.
"She played really well throughout the whole match," she said. "I know what she is capable of so I was prepared.
"She plays a little bit differently so I was happy I could adapt and find my best tennis when it was necessary."
Azarenka said she maintained the passion for the game she had when she first picked up a racquet as a youngster.
"I always had that fire, I would never leave the court until 10pm," she said.
"I wish every kid was like that."
Kuznetsova grabbed the first service break to lead 3-1 in the opening set as Azarenka's return bounced wide.
But the Belarusian was handed it back in the seventh game when Kuznetsova double-faulted.
She again broke to lead 6-5 with a cross-court return and went on to take the set in 77 minutes.
Azarenka broke serve in the fifth game following another crucial double fault from Kuznetsova, took a 5-1 lead and then broke again for the match.
The pair had met seven times previously and, while Kuznetsova held a 4-3 record, she dominated their early encounters. But Azarenka has held the upper hand in recent matches, beating the Russian twice last year, at Indian Wells and in Madrid.
Kuznetsova was sidelined for much of 2012 with a knee injury and was on crutches for two months.
However, the 27-year-old, who admitted she was jaded last year, made a determined bid to return refreshed for 2013. She came into the Australian Open after reaching the quarter-finals in Sydney as a qualifier.
