She beat Azarenka all five times they played last year, and is 11-1 in career head-to-heads against the 23-year-old Belarusian.
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.
Asked if it helped to have her No. 1 fan wearing a keep calm logo, Azareka said "I was looking more at the part that says 'Bring out the bottles.' "
Of her game, she added, "I'm just glad I could produce my good tennis when it was needed."
In the men's quarterfinals, 17-time major winner Roger Federer was playing No. 7 Jo-Wilfried Tsonga in a night match and U.S. Open champion Andy Murray was to meet Jeremy Chardy of France.
Novak Djokovic is already through the semifinals after his 6-1, 4-6, 6-1, 6-4 win over fifth-seeded Tomas Berdych on Tuesday night.
The 2-hour, 31-minute victory took exactly half the time of his five-set, fourth-round win two nights previously against Stanislas Wawrinka.
"It was a great performance. I was hoping to have a shorter match ... just not to go over 5 hours," Djokovic said, in a comparatively subdued mood Tuesday after a considerably more routine victory. "It's always going to be tough against Tomas; he's an established player. He has a big game, big serve. He can compete against anyone on any surface."
In the semifinals, Djokovic will meet No. 4-seeded David Ferrer.
O Defending champion Victoria Azarenka beat Svetlana Kuznetsova 7-5, 6-1.
• Azarenka will face the winner of a match between Serena Williams and Sloane Stephens.
O Quarterfinals, noon (tape), ESPN2
• Women's semifinals, 7:30 p.m., ESPN2
• Men's semifinal, 1:30 a.m., ESPN2