Ashleigh Barty returns a shot to Aryna Sabalenka during the Miami Open on Tuesday. Photo: VCG

World No.1 Ashleigh Barty advanced to the semifinals of the Miami Open on Tuesday as Russian top seed Daniil Medvedev booked his place in the quarterfinals of the men's tournament.

Barty battled through her third three-setter of the fortnight to oust seventh-seeded Aryna Sabalenka of Belarus in two hours and 16 minutes on the Grandstand Court.

The Australian will face Elina Svitolina of Ukraine in the semifinals following her gruelling 6-4, 6-7 (5/7), 6-3 win. 

Fifth seed Svitolina advanced to the last four after defeating Latvia's Anastasija Sevastova 6-3, 6-2 later Tuesday.

After taking a close first set, Barty appeared to be on the brink of victory after grabbing a 3-1 lead in the second set tie-break.

Sabalenka staged a superb recovery however to snatch the tiebreaker 7-5, forcing a decisive third set.

Barty regrouped in the third though and with Sabalenka clearly in pain clutching her stomach, rammed home her advantage to complete a deserved win.

The victory leaves Barty one semifinal win away from retaining her world No.1 ranking, though the Australian insisted she was not preoccupied with holding on to top spot.

"It's an amazing thing to be No.1 in the world at the moment, but I promise you that's not what makes me happy," Barty said afterward.

"It's a focus of course. I want to try to do the best that I can, but it's not a distraction or a pressure in any way."

Medvedev meanwhile had an easier ride in the men's tournament, easing past Frances Tiafoe of the United States in straight sets, 6-4, 6-3.

Medvedev hammered down 11 aces in the win, breaking Tiafoe three times en route to victory.

Medvedev will face Roberto Bautista Agut in the last eight after the Spaniard eliminated John Isner in three sets to avenge his 2019 quarterfinal loss in Miami.

Bautista Agut saved a match point at 5-6 down in the third set tiebreaker to claim a 6-3, 4-6, 7-6 (9/7) win.

The biggest upset of the day saw world No.87 Sebastian Korda continue his giant-killing run by knocking out Argentina's fifth seed Diego Schwartzman, winning 6-3, 4-6, 7-5.

"I played an incredible match today," said Korda, the Florida-born son of former Australian Open champion Petre Korda.

Korda will face Russia's fourth-seeded Andrey Rublev in the last eight. Rublev reached the quarters with a 6-4, 6-4 defeat of Marin Cilic.

In other last-16 matches on ­Tuesday, Italy's 21st-seeded Jannik ­Sinner downed Finland's Emil Ruusuvuori 6-3, 6-2 to advance to the last eight.

It is the first time the 19-year-old has reached the quarter-finals of an ATP Masters event.