Australian Open: Serena Williams makes shock exit
In tomorrow's semi-finals, Stephens will face top seed Azarenka, who came through a marathon, 1hr 17min opening set against Kuznetsova before completing her 7-5 6-1 triumph in 1hr 47min.
The first game was a drawn-out scrap, lasting eight minutes and going to Russian comeback queen Kuznetsova, a two-time major-winner who is making a successful return from injury.
She survived pressure in her opening two service games and broke Azarenka in a fourth game that stretched to 15 minutes and included 10 deuces. After 34 minutes, only four games had been completed, with Kuznetsova leading 3-1.
Azarenka then trailed 1-4 but she broke back to 3-4 as errors crept into Kuznetsova's previously steady onslaught. Another break gave Azarenka a 6-5 lead and she held her nerve to close the set.
The Belarusian began motoring to victory when she broke Kuznetsova's opening serve of the second set. She immediately conceded her own serve, but another break was exchanged and that was the end of Kuznetsova's resistance, as Azarenka finished the match with a barrage of groundstroke winners.
"She played really well throughout the whole match," Azarenka said. "At the beginning, it took adjustment because she plays such a different game.
"I'm glad I fought through and produced my best tennis when it was needed."
Murray strolls into last four at Melbourne Park
Andy Murray ruthlessly dismissed unseeded Frenchman Jeremy Chardy 6-4 6-1 6-2 to reach the Australian Open semi-finals for the fourth year in a row on Wednesday.
The third seeded Briton had spent just over seven hours on court in his previous four matches and only needed another 111 minutes to complete a one-sided hammering of the world number 36.
Chardy had won the last meeting between the two in Cincinnati in August but another upset was never on the cards and the U.S. Open champion wrapped up victory when the Frenchman ballooned a forehand into the sky on Rod Laver Arena.