Stephens prevailed 3-6 7-5 6-4 to set up a semi-final against world number one Victoria Azarenka, the 19-year-old maintaining her focus to see out the victory after the five-time champion had jarred her back in the second set and left the court for medical treatment.
"Oh my goodness," an emotional Stephens said in a courtside interview as she secured a maiden grand slam semi-final berth. "I'm sure my grandparents are freaking out. I'm sure they're watching on the computer."
The match was billed as a showdown pitting the future of American tennis against the most accomplished player of the present generation, and the early signs indicated that Williams possessed too much power for her younger opponent.
Both players hammered away at each other on serve in the opener with the receiver winning a total of two points until the eighth game, when Williams broke Stephens to take a 5-3 lead then held to seal the set in 28 minutes.
The nature of the contest changed dramatically when Williams, already concerned by an ankle injury sustained in the first round, appeared to twinge her back when chasing a drop shot in the eighth game of the second set.
Visibly in pain, the 31-year-old's vigour disappeared and she took a medical timeout to have the injury assessed. Tournament officials said she was suffering from spasms.
The 15-times Grand Slam champion, who had looked in such distress that it appeared she would retire from the match, somehow returned but there was no zip to her serve.
Averaging more than 170kph throughout the tournament and with several serves in excess of 200kph, the American was barely able to roll her shoulder over, with the sole aim of getting the ball into the service box to begin rallies.
By contrast, Stephens, appeared to suffer a mental block, getting broken when she was serving for the set while Williams, who was now serving less than 130kph, held to love as the slower paced deliveries affected the teenager's timing.
Stephens, however, managed to regain her composure and win the next two games to take the set 7-5 and level the match.
Frustrated and in pain, Williams let her anger boil over at the end of the third game of the decider after Stephens had taken a 2-1 lead.
Williams twice smashed her racquet into the court and hurled the broken equipment under her chair and the momentary outburst of destruction appeared to work in her favour as she cranked up the speed of her serve again.
Looking more comfortable in her movement, Williams broke to make it 4-3 in the decider but was unable to prevent her gutsy opponent from breaking back immediately.
Stephens then held and broke again to seal the shock victory and set up a semi-final against defending champion Azarenka after the Belarusian had beaten Svetlana Kuznetsova 7-5 6-1 in the early match on Rod Laver Arena.
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