The 31-year-old Williams needed less than an hour to advance under lights at Rod Laver Arena with a 6-2 6-0 victory, and will meet another woman in a hurry in teenager Stephens.
The wise-cracking 19-year-old has been touted as an heir to the 15-times Grand Slam champion Williams and bolstered her credentials with a mature 6-1 3-6 7-5 win over Serbia's Bojana Jovanovski in the afternoon sun at Hisense Arena.
But Williams fired a warning shot ahead of the generational battle, with her serve on fire and after bashing 22 winners against the 14th-seeded Russian.
"I think she's playing great," Williams said courtside of Stephens. "I think she has incredible talent, I actually admire her as well.
"I feel like I have nothing to lose and I'm just going to have fun when I play."
Williams twisted her ankle in her first round clash against Romania's Edina Gallovit's-Hall, but still breezed through the first three rounds at Melbourne Park dropping just a total of six games.
The 31-year-old's power game was again to the fore against Russia's Kirilenko with the American clocking a 201-kph serve, getting almost 90 percent of her first serves in during the 57-minute clash.
Stephens was just happy to advance to her maiden Grand Slam quarter-final, and secured a A$250,000 payday when her shrieking opponent duffed a return into the net.
"I'm sure my mum's had, like, four heart attacks," Stephens said courtside, raising a laugh from the crowd.
"I try to save all my money because I don't want to be old and broke. I'm still trying to save my money but I'll definitely buy something nice."
"I think mentally it was pretty tough... I was playing my own self, I guess you could say. But I managed to get through, so that was good."
Stephens may still be a teenager, using "like" as form of punctuation in her media conferences and peppering her game with shots that exhibit the capriciousness of youth, but the mental toughness belies her age.
That toughness was evident three years ago when her birth father, former NFL running back John Stephens, was killed in a car crash shortly before the US Open.
She attended his funeral then returned to New York for qualifying, though lost in the first round.
Since then she has had a meteoric rise up the rankings, cracking the top-200 at the end of 2010 and the top-100 in September 2011.
Last year, however, was her break out year as she made two WTA tour semi-finals at Strasbourg and Washington and broke into the top 50.
By year's end she was 38th, the highest-ranked teenager in the world and had made a friendly bet with training partner Sam Querrey as to who would finish higher in 2013.
Querrey was seeded 20th for the Australian Open, but crashed out in the third round. Stephens will now move into the top-20 after her quarter-final appearance.
"Yeah, we'll bet on who is going to be in the top 20 first, all this other stuff," Stephens added with a grin.
"I'm like, 'I'm not even going to be seeded in Australia. I could get number one seed. There's no hope for me'."
"(But) he's never been in the quarters of a Grand Slam, so... I got him."
Stephens is the first American woman other than Serena or Venus Williams to make a Grand Slam quarter-final since Melanie Oudin made the last eight at the 2009 US Open.
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