Stephens has said she had a photo of Williams in her room when she was a child, and had long admired the Williams sisters.
"This is so crazy. Oh my goodness," Stephens said, wiping away tears in her post-match TV interview. "I think I'll put a poster of myself (up) now."
Azarenka, with her most famous fan sitting in the crowd wearing a shirt reminding her to keep calm, overcame some early jitters to beat Kuznetsova.
After dropping serve in a long fourth game that went to deuce 10 times, Azarenka recovered to dominate the rest of the match against Kuznetsova, a two-time major winner who was floating dangerously in the draw with a No. 75 ranking as she recovers from a knee injury.
Azarenka's American rapper friend, Redfoo, returned from a concert in Malaysia to attend Wednesday's quarterfinal match.
Wearing a red sleeveless T-shirt that read "Keep Calm and Bring Out the Bottles," the name of his next single, Redfoo stood, clapped and yelled "Come on, Vika!" during the tight first set.
Williams' loss was a boost for Azarenka, who lost all five head-to-heads against the American in 2012 and is 1-11 in their career meetings.
The 25-year-old Murray had his service broken for only the second time while serving for the match. But he broke back immediately to clinch a quarterfinal victory.
Murray discounted comments in the British media that he was upset with an almost full schedule of day matches while Federer was given featured cooler night slots on Rod Laver Arena.
"The scheduling for me is part and parcel of playing in really any tennis tournament," Murray said. "It's tough to make the schedule perfect for every single player."
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