After a tentative start, the 19-year-old went toe-to-toe with an injury-hampered Williams on Rod Laver Arena on Wednesday to claim a 3-6 7-5 6-4 win and set up a semi-final with defending champion Victoria Azarenka.
Hailed as the future of American tennis, Stephens said she needed time to convince herself she could send 31-year-old Williams packing from the first Grand Slam of the year.
"Last night I was thinking about it and ... someone asked me like, 'Do you think you can win?' I was like, 'Yeah, I think so', but I wasn't too clear about it," Stephens said after pulling off the biggest upset of this year's tournament.
"Then this morning when I got up, I was, 'Look, dude, you can do this. Go out and play and do your best.'"
Stephens took heart after fighting back from 2-0 down in the second set after losing her serve, and began going for broke against the 15-times Grand Slam champion.
"From then on I got aggressive, started coming to the net more, and just got a lot more comfortable," she said.
"I just kind of played my game from there, I think."
Stephens had to "chillax" as Williams took a lengthy medical time-out to deal with a back injury and watched as her opponent took out her frustrations by destroying a racket in the third set.
The release of anger appeared to help Williams, who broke to lead 4-3 in the decider, but the Florida-born Stephens showed great poise to break back immediately and go on to seal the match when Williams netted a backhand.
Like a typical teenager, it was not long before Stephens was checking her phone to find more than 200 messages of congratulations. She also found the number of followers on her Twitter account had doubled.
"I had 17,000 (followers), now I have 35,000," said Stephens, who is now A$500,000 richer for reaching the last four.
Among the Tweets was one from four-times Grand Slam champion Kim Clijsters: "Just woke up to great news! Have been a fan of you for a couple years now! Well done girl! Stay cool en go all the way x."
Stephens was concerned about how to respond to all her well-wishers, with worries about the phone bill.
"I'm still trying to figure that out because I thought it was free to receive text messages, but someone told me otherwise," she said.
"So I'm still trying to figure out what I'm going to do, because otherwise my phone bill is going to be crazy and my mom is going to be like, 'Oh, my God, your phone bill'.
"She's going to be like, 'The money you were going to buy yourself something nice with, you're going to pay your phone bill.'"
The realisation that she had dumped the greatest player of her generation out of the tournament sunk in while she was stretching after the match.
"I was like, 'I'm in the semis of a grand slam'," she said. "I was like, 'Whoa'. It wasn't as hard as I thought. But it's pretty cool."
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