MIAMI: World number one Ashleigh Barty advanced to the semi-finals of the Miami Open on Tuesday as Russian top seed Daniil Medvedev booked his place in the quarter-finals of the men's tournament.

Barty battled through her third three-setter of the fortnight to oust seventh seeded Aryna Sabalenka of Belarus in 2hr 16min on the Grandstand Court.

The Australian will face either Latvia's Anastasija Sevastova or Elina Svitolina of Ukraine following her gruelling 6-4, 6-7 (5/7), 6-3 win.

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 tie-break 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 semi-final win away from retaining her world number one 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 afterwards.

"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."