MIAMI — Ash Barty is tough to beat under any circumstances, especially when she's on the ropes.

She proved that again Monday.

The world's top-ranked player has reached the Miami Open quarterfinals, getting there by holding off 14th-seeded Victoria Azarenka of Belarus 6-1, 1-6, 6-2. It was Barty's 17th win in her last 20 three-set matches, two of those victories for the Australian coming so far in this tournament.

"That's a cool stat," Barty said.

This, too, was cool: The match lived up to its showdown potential, with the reigning Miami Open champion and current world No. 1 in Barty facing someone who has won the Miami title three times and a previous world No. 1 in Azarenka.

Barty rolled in the first set, Azarenka in the second. But the third — as they tend to be — was all Barty, who was never in trouble in the deciding set.

"It's just about staying in the fight," Barty said. "It's about not relenting, not giving up regardless of whether you lose a set or you get a break, whatever it might be. I think it's just about trying to hang around and I've worked my backside off off the court to make sure that I feel like I'm good physical condition to play tennis."

No. 5 seed Elina Svitolina of Ukraine needed nearly 2½ hours to beat ninth-seeded Petra Kvitova of the Czech Republic 2-6, 7-5, 7-5 and earn her ticket to the quarterfinals.

"It was not easy conditions," said Svitolina, who has already matched her best Miami finish by making the quarters. "I was trying to fight, trying to find a way, one extra ball over the net."

Barty will next face No. 7 seed Aryna Sabalenka, a 6-1, 6-2 winner over No. 19 seed Marketa Vondrousova. Svitolina will play unseeded Anastasija Sevastova of Latvia in the quarters; Sevastova was a 6-1, 7-5 winner over wild-card Ana Konjuh of Croatia.

No. 2 women's seed Naomi Osaka of Japan ran her winning streak to 23 matches and moved into the quarters by topping No. 16 seed Elise Mertens of Belgium, 6-3, 6-3. 

"I'm not the type of player that really needs that many tournaments to feel a groove," Osaka said.

Osaka wasted six set points before finally finishing off Mertens to win the opening set; she needed five break points before cashing in to go up 2-1 in the second. Mertens later needed a medical timeout that lasted about 10 minutes while she left the court to get treatment on the area below her right shoulder.

She didn't win another game; Osaka casually munched on a banana and took a few serves while waiting for Mertens to return, then cruised the rest of the way. Osaka next meets No. 23 Maria Sakkari of Greece, who won a 2-hour, 38-minute marathon over No. 29 Jessica Pegula of the U.S.

Sakkari fended off six match points and won 6-4, 2-6, 7-6 (6).

Unseeded Sara Sorribes Tormo of Spain got her fourth win of the tournament, all of them three-setters. She topped No. 27 seed Ons Jabeur of Tunisia 6-4, 0-6, 6-1.

Next up for Tormo: No. 8 seed Bianca Andreescu of Canada, a 3-6, 6-3, 6-2 winner over No. 12 seed Garbine Muguruza of Spain in Monday's final match — capping a day where five of the eight women's matches went three sets.

"I'm playing the best tennis of my life, this is for sure," Tormo said after her shortest match of the tournament — a mere 2 hours.

On the men's side, Sebastian Korda of the U.S. got his second consecutive win over a seeded foe, this one a 6-3, 6-0 romp past No. 17 Aslan Karatsev of Russia. Korda's reward is a matchup with No. 5 seed Diego Schwartzman of Argentina in the round of 16.

Korda is one of four U.S. men in the round of 16 at Miami. His father, Petr Korda, played in the event 10 times at its former Key Biscayne home and made the round of 16 on four occasions.

"It's cool and it's been super-special for sure," the younger Korda said of having Miami success.

No. 26-seeded Hubert Hurkacz of Poland upset sixth-seeded Denis Shapovalov of Canada 6-3, 7-6 (6). Shapovalov was clearly frustrated with some calls that the Hawk-Eye Live technology — the system that replaces live lines judges with cameras — saw one way and he saw another way.

"We're getting used to that, that Hawk-Eye life," Hurkacz said. "It's a little bit different."

No. 2 seed Stefanos Tsitsipas of Greece topped No. 28 Kei Nishikori of Japan 6-3, 3-6, 6-1. Tsitsipas meets No. 24 Lorenzo Sonnego of Italy, a 7-6 (6), 6-3 winner over Daniel Elahi Galan of Colombia.

In other third-round men's matchups, Schwartzman defeated 25th-seeded Adrian Mannarino of France 6-1, 6-4; 12th-seeded Milos Raonic of Canada topped 20th-seeded Ugo Humbert of France 6-4, 7-5; and 2014 U.S. Open champion Marin Cilic of Croatia defeated Italy's Lorenzo Musetti 6-3, 6-4.

Cilic will meet fourth-seeded Andrey Rublev of Russia next. Rublev rolled past Hungary's Marton Fucsovics 6-2, 6-1 — beating him head-to-head for the third time in the last 22 days, and that doesn't even include a walkover victory over Fucsovics in Qatar in that span.

"Marton (told) me, 'I don't want to see you. I don't want to see you,'" Rublev said.