Kvitová of the Czech Republic has won in Madrid more times than any other woman, having lifted the women's singles trophy in 2011, 2015 and 2018.

But the two-time major winner was forced to dig deep to reach her sixth career quarter-final at the event in the Spanish capital as she overcame Russia’s Kudermetova 6-3, 4-6, 6-4.

Ninth seed Kvitová will next meet world number one Ashleigh Barty of Australia.

Barty, who won the French Open in 2019 but did not play in the world's premier clay-court tournament in 2020 because of the coronavirus crisis, defeated current French Open champion Iga Świątek of Poland 7-5, 6-4.

The Australian saved six of seven break points en route to beating 19-year-old Świątek. 

Switzerland’s Belinda Bencic moved into the last eight after a right thigh injury forced Ons Jabeur of Tunisia to retire trailing 7-6 (7-2), 4-3.

Bencic will now face either wildcard Paula Badosa of Spain.

In the men’s event, South African Lloyd Harris marked his Madrid Open debut with a 6-3, 3-6, 7-6 (7-5) victory over 13th seed Grigor Dimitrov of Bulgaria.

Harris failed to convert three match points on Dimitrov’s serve when 5-2 in front in the deciding set.

He was subsequently broken but won four straight points from 3-2 down in the tiebreak.

American John Isner worked his way past Miomir Kecmanovic of Serbia with a 6-4, 7-6 (8-6) success.

Carlos Alcaraz booked a dream all-Spanish second-round encounter against five-time champion Rafael Nadal.

The Spaniard, who will celebrate his 18th birthday on Wednesday (May 5), ripped 19 forehand winners en route to a 6-4, 6-0 win against France’s Adrian Mannarino.

"For me, [to] play against Rafa is a dream come true," Alcaraz said.

"Since I was a kid, I wished to play a match against Rafa and now I will be able to here [on] the Centre Court of La Caja Magica in Madrid.

"It is a really special match against Rafa."

Italy’s Fabio Fognini booked a second-round meeting with countryman Matteo Berrettini after seeing off Spanish qualifier Carlos Taberner 7-6 (7-4), 2-6, 6-3 in 2 hours and 15 minutes.

Russia’s Aslan Karatsev opened his debut Madrid Open campaign with a 7-5, 6-4 victory against Frenchman Ugo Humbert.

Britain’s Dan Evans earned his third win of the season against France’s Jeremy Chardy.

The Monte-Carlo Masters semi-finalist withstood 35 forehand winners from his opponent to record a 7-6 (8-6), 6-7 (7-9), 6-2 triumph after 2 hours and 46 minutes.

More follows.