Third seed Williams, gunning for her sixth Australian title, blitzed a dazed Maria Kirilenko 6-2, 6-0 and has conceded just eight games in the tournament so far.
That equalled the previous record held by Monica Seles and Steffi Graf, but Williams’ main rival Maria Sharapova has already set a new mark by getting to the same stage by losing just five games.
The two are scheduled to meet in the final.
Williams summed up her performances so far as “consistency, fighting”.
“I’m really out there just doing the best I can, just fighting for everything,” she said. “I think with that attitude I’m just trying to stay in the tournament just to stay alive.”
She next faces exciting American teenager Sloane Stephens, who beat Serb Bojana Jovanovski in a tough 6-1, 3-6, 7-5 battle to make her first Grand Slam quarter-final.
Like Williams, top seed Azarenka took less than an hour to dispose of Elena Vesnina 6-1, 6-1 to set up a last eight meeting with Kuznetsova, a two-time Grand Slam winner who spent two months on crutches last year.
The experienced Russian needed a tense 2hrs 28mins to oust 10th seed and former world number one Caroline Wozniacki 6-2, 2-6, 7-5.
“I can see Sveta came back much fresher, much stronger,” Azarenka said of her clash with Kuznetsova.
“She knows how to handle big stages, big tournaments. She’s a Grand Slam champion. It’s definitely an exciting match for me to be in.”
The Belarusian world number one was in red-hot form off the baseline against Russia’s unseeded Vesnina, but seven double-faults blotted her performance.
Kuznetsova has dropped down the rankings to be 75 in the world, but she showed her quality against Wozniacki, who has been struggling for form.
It was a courageous win by the Russian after an injury to her right knee forced her to skip a big chunk of 2012.
The injury meant she missed all post-Wimbledon events including the US Open, which ended her streak of 40 straight Grand Slam appearances dating back to 2002 at Flushing Meadow.
But Kuznetsova, who won the 2004 US Open and 2009 French Open, said she was feeling fresh again.
“I never had a thought of stopping tennis. I was just laying in bed, and I was like, thanks knee. At least I can rest,” she said.
The defeat was another disappointment for Wozniacki, whose preparations for Melbourne were hurt by going out early at both the Brisbane and Sydney International tournaments.
“There is still a long year in front of me. There are still a few things I can work on and it can be better,” said the Dane, whose golf-star boyfriend Rory McIlroy also had a poor start to his season, missing the cut in Abu Dhabi.
On Hisense Arena, Stephens was made to dig deep for her first appearance in a last eight at a major.
The 19-year-old, whose poise and power has seen her compared to a young Williams, steamrolled through the first set before Jovanovski woke up and gave her a fright.
“I don’t know what happened after the first set but she played great tennis,” said Stephens.
“I haven’t beaten Serena and I hope I’ll give you all a good show.”
Sheikh Mohamed said solving the challenges facing the planet requires a shared vision
Williamson hit 104 off 205 balls in his 29th Test century with 11 fours
The draw for the $1,000,000 grand prize is set to take place live on December 2