Madrid Open: Rafael Nadal through to quarter-finals; Ashleigh Barty beats Paula Badosa

Madrid: Rafael Nadal swept into the Madrid Open quarter-finals on Thursday with a 6-3, 6-3 victory over Alexei Popyrin, while Ashleigh Barty booked her spot in the women's final by ending the run of wildcard Paula Badosa.

Nadal, a five-time champion in the Spanish capital, saved five of six break points in a challenging opening set as he faced the 76th-ranked Popyrin for the first time.

A lone break of the Australian's serve in the second was enough for the 20-time Grand Slam winner to seal the match and set up a showdown with fifth seed Alexander Zverev or Britain's Dan Evans.

Evans upset Novak Djokovic earlier this month at Monte Carlo, where Nadal lost in the quarters to Andrey Rublev. The Spaniard recovered from that setback to win his first title of the year in Barcelona last week.

Dominic Thiem, the Madrid runner-up in 2017 and 2018, also reached the last eight after beating Alex de Minaur 7-6 (9/7), 6-4.

US Open champion Thiem, playing his first tournament since Dubai in March, will meet Rublev or John Isner in the next round.

Thiem lost his serve in the opening game but recovered with a break for 3-all. He missed a set point in the tie-break and then saved one before clinching the first set at the second attempt.

The Austrian third seed withstood three break points early in the second set and then broke De Minaur the following game.

De Minaur, the world number 24, hit back to level at 3-all but promptly dropped serve the next game as Thiem secured victory in just under two hours.

"I feel way better than expected. In some points and some rallies, I still feel the lack of matches," Thiem said, a two-time finalist in Madrid.

"I am a little bit more out of breath, I am a little bit too tight in some shots and some strokes."

"I have to get back in a rhythm, but the more matches I play against these top guys, the quicker I will get back in the match rhythm I need," he added.

Medvedev out as Barty keeps going

World number three Daniil Medvedev exited in the last 16 following a 6-4, 6-7 (2/7), 6-1 defeat by 16th seed Cristian Garin of Chile.

Medvedev had won his first match in Madrid in his third appearance on Wednesday, but the Russian was sent packing by an opponent far more at ease on clay.

The two-time Grand Slam runner-up heads to Rome next. He has never won a match in the Italian capital, and he has failed to get past the first round of the French Open in four previous tries.

Alexander Bublik of Kazakhstan progressed to the quarter-finals with a 6-4, 6-3 win over in-form Russian Aslan Karatsev.

Barty cruised into the women's final with a 6-4, 6-3 victory over Badosa, as the world number one avenged last month's loss to the Spaniard in Charleston.

Barty, the 2019 French Open champion, is targeting a fourth title of the year following her wins at Melbourne's Yarra Valley Classic, in Miami and on clay in Stuttgart.

Ashleigh Barty in action against Paula Bados at Madrid Open. AFP

The top seed shaded a tight opening set against the 62nd-ranked Badosa, the first Spanish woman in the tournament's 12-year history to make the semi-finals.

She converted her third set point when Badosa doubled faulted at 4-5, a single break of serve proving decisive for the Australian.

Barty dropped serve herself to start the second set but broke twice in succession to regain control and make it 16 straight wins on red clay.

She will play fifth seed Aryna Sabalenka of Belarus or Russia's Anastasia Pavlyuchenkova in Saturday's final.