MELBOURNE, Australia -- Serena Williams has returned to the Australian Open quarterfinals by getting past No. 7 seed Aryna Sabalenka in three sets, while Naomi Osaka fought off two match points to eliminate Garbine Muguruza in a big-hitting fourth-round matchup of Grand Slam champions on Sunday.
The 6-4, 2-6, 6-4 victory put Williams one step closer to her record-tying 24th Grand Slam title overall and eighth championship at Melbourne Park.
Her most recent major trophy came at the Australian Open in 2017, while she was pregnant.
Williams will play Simona Halep, who advanced after beating French Open champion Iga Swiatek 3-6, 6-1, 6-4.
The No. 2-seeded Halep avenged a loss last year at Roland Garros, where Swiatek dropped just three games in their fourth-round match.
After accounting for the last remaining teenager in the draw, two-time major winner Halep will now meet one of the most experienced players on tour. Halep lost the final at Melbourne Park in 2018 and reached the semifinals here last year.
This was Williams' 62nd fourth-round match at a major tournament -- and Sabalenka's second.
They played a similar brand of powerful tennis, but Williams was barely better, stealing the last two games after what had been a 4-1 lead in the final set evaporated.
"I am happy to get through that one. It wasn't easy," Williams said. "She was teeing off on every shot.''
Williams ended up with more winners, 30-24, and more aces, 9-4, while cranking up her best-in-the-game serve to as fast as 126 mph.
When Williams needed to volley, she did -- and rather well, claiming 13 of 15 points when she went to the net. More importantly, she covered the court much in the way she did in her younger days, when opponents' apparent winners were rendered mere fodder for her own strikes.
And she showed no signs of trouble from the left Achilles tendon that hampered her in a US Open semifinal loss in September and forced her to withdraw from the French Open before the second round later that month.
"I've worked really hard on my movement. Yeah, I like retrieving balls. I mean, obviously, I like to be on the offense, but I can play defense really well, as well,'' the 39-year-old American said. "I didn't think about my Achilles. It's so good to not think about it. Oh, my goodness.''
Sabalenka -- a 22-year-old from Belarus playing in only her second fourth-round Slam match -- was visibly and audibly frustrated. She frequently would scream after lost points. She spiked her racket, too.
Bleak as things looked for her late in a matchup of former No. 1-ranked women, Osaka never wavered, erasing two match points and grabbing the last four games to edge Muguruza 4-6, 6-4, 7-5 at Rod Laver Arena.
The third-seeded Osaka returns to the quarterfinals of a tournament she won in 2019 for one of her three major trophies. Osaka ran her winning streak to 18 matches -- a stretch that included a US Open title in September -- and put a stop to Muguruza's own fine form of late.
Heading into Sunday -- the second day of the tournament without any spectators because of a local COVID-19 lockdown -- two-time major champion Muguruza had been broken only once in this Australian Open. She had dropped a total of 10 games through three matches.
But Osaka broke her five times and won 17 games in all in a contest featuring entertaining baseline back-and-forth play and terrific serving by both on a cloudy day with temperatures in the mid-60s.
"I was a bit intimidated, because I knew that she was playing really well coming into this match,'' Osaka said. "In the stressful points, I feel like I just had to go within myself. And I know that today I probably hit a lot of unforced errors, but I feel like it was what I needed to do, because I couldn't really give her any short balls because she would finish it.''
Osaka wound up with more unforced errors, 36-28, but also more winners, 40-24.
The key moment came when Osaka was serving at 15-40 while trailing 5-3 in the final set. Muguruza could not convert either of those match points: Osaka delivered one of her 11 aces at 118 mph on the first; Muguruza missed a groundstroke on the second.
Fifteen minutes later, the match would be over.
Muguruza served for the win in the next game and got broken when Osaka smacked a crosscourt forehand winner to close a 14-stroke exchange. After holding to go up 6-5, Osaka broke Muguruza yet again to win their first head-to-head meeting.
Osaka, a 23-year-old who was born in Japan and moved to the United States with her family when she was 3, now faces unseeded 35-year-old Su-Wei Hsieh of Taiwan with a semifinal berth at stake.
"I'm not really looking forward to it,'' Osaka said. "She's going to be really tough.''
The 71st-ranked Hsieh's 6-4, 6-2 victory over 2019 French Open finalist Marketa Vondrousova made her the oldest woman to make her major quarterfinal debut in the professional era.
This is Hsieh's 38th main-draw appearance at a Grand Slam tournament.
Hsieh plays with an unusual style that includes two-handed shots off both sides, and that might have flustered the 19th-seeded Vondrousova, who made 31 unforced errors, 13 more than the winner.
Hsieh beat 2019 US Open champion Bianca Andreescu in the second round.
The Associated Press contributed to this report.