Serena Williams ground down top seed Simona Halep in an epic three-setter to take her quest for a record-equalling 24th major into the Australian Open quarter-finals on Monday.

The 37-year-old American beat the Romanian world number one 6-1, 4-6, 6-4 to set up a last eight clash with Czech eighth seed Karolina Pliskova.

Japanese fourth seed Naomi Osaka edged past 13th seed Anastasija Sevastova of Latvia in three sets last eight as well.

The US Open champion triumphed 4-6, 6-3, 6-4 to set up a last eight clash with Ukrainian sixth seed Elina Svitolina and keep alive her dream of a second successive Grand Slam title.

The 24-year-old Svitolina dug deep to overcome 17th seeded American Madison Keys in three sets to reach the quarter-finals for the second time in a row.

Czech seventh seed Karolina Pliskova marched into the Australian Open quarter-finals for the third straight year Monday with a commanding straight sets win over 18th seed Garbine Muguruza of Spain.

Pliskova triumphed 6-3, 6-1 to set up a last eight meeting with either world number one Simona Halep or 23-time Grand Slam champion Serena Williams.

It is the second time in a row the 21-year-old had been forced to come back from a set down after struggling to overcome Taiwan’s Hsieh Su-Wei in the previous round.

Osaka had to compose herself at times on court against the dogged Sevastova, who went into the match with a 2-2 record against the 21-year-old. She had beaten the Latvian in a tight three-setter at the quarter-finals of the Sydney International this month and Sevastova appeared intent on exacting revenge on the Grand Slam stage.

The 28-year-old broke early in the opening set, holding on to the advantage to maintain pressure on her younger opponent. Osaka buried her head in her hands and mumbled to herself as she served to stay in the set at 5-3.

She managed to hold but could not prevent Sevastova serving the set out at 6-4 in 31 minutes.

With her shot at a second Grand Slam on the line, Osaka was much improved in the second set, cutting her error rate and hitting 18 winners to five. She managed to force a deciding set, making the perfect start with a break over Sevastova.

Shaking off the Latvian proved a difficult task though, as Sevastova put the set back on level terms at 3-3 after bringing up six break points. Osaka managed a crucial break back in the next game and held on for victory.

The 26-year-old Pliskova has been a regular in the second week of Slams in recent years, reaching the quarters or better seven times since late 2016 while still searching for a breakthrough win.

But she said Melbourne Park was her favourite venue after also reaching the quarters in 2017 and 2018. She entered this year’s event on a high after winning the Brisbane International warm-up

She went into the match with a 7-2 winning record over Muguruza and always looked confident against the Spaniard.

Muguruza never settled and committed 20 unforced errors in the match.

The Spaniard had endured a physically draining late clash with Briton Johanna Konta in the third round that set a tournament record after it began in the early hours of Friday morning.

Keys, a US Open finalist in 2017, started slowly but came back to take the second set and put Svitolina under pressure at the start of the third.

The turning point was a marathon 16-minute game early in the deciding set that went to deuce 11 times as Keys chased a decisive break. But the American’s resolve crumbled when Svitolina held off five break points then gained an advantage in the next game.

Svitolina was a quarter-finalist at Melbourne Park last year and has made the last eight at Roland Garros twice but is yet to progress further in a Grand Slam.

She has set her sights high this year after her breakthrough in Singapore, targeting a Grand Slam win and world number one. Svitolina pounced as Keys came out of the blocks slowly and raced to a 4-0 lead in the opening set with a double break.

The Ukrainian, who lost her previous two meetings with the American, struggled in the second as Keys stepped up her aggression, coming to the net and adding extra venom to her returns.

The American was rewarded with a double break taking the set 6-1 after 23 minutes.

The early stages of the decider developed into a dogfight before Svitolina prevailed over the frustrated Keys.

Results

Women’s singles

4th round

Naomi Osaka (JPN x4) bt Anastasija Sevastova (LAT x13) 4-6, 6-3, 6-4

Elina Svitolina (UKR x6) bt Madison Keys (USA x17) 6-2, 1-6, 6-1

Karolina Pliskova (CZE x7) bt Garbine Muguruza (ESP x18) 6-3, 6-1

Serena Williams (USA x16) bt Simona Halep (ROM x1) 6-1, 4-6, 6-4