Rafael Nadal saw off Alexei Popyrin to reach the Madrid Open quarter-finals on a day that saw Daniil Medvedev and Stefanos Tsitsipas suffer surprise defeats.

World number two Nadal, chasing a record-extending sixth title on home soil, advanced 6-3 6-3 in a time of one hour and two minutes on Thursday.

Popyrin, playing in his first last-16 match at a Masters 1000 event, broke Nadal in the sixth game of the opening set but the Spaniard otherwise looked comfortable.

Nadal converted four of his six break points to advance through to the last eight for a 15th time, where Alexander Zverev awaits.

"It was difficult," Nadal said in his on-court interview. "The court today was slippery, it was very fast, very dry conditions. The ball was flying a lot. The beginning was super tough. 

"He was hitting every ball and hitting the spots. I'm happy with the victory. It was an important victory, he came here playing well. Every match is tough."

Zverev, who won the competition in 2018, beat British number one Dan Evans 6-3 7-6 (7-3) to set up a meeting with Nadal

However, second and fourth seeds Medvedev and Tsitsipas saw their participation come to an end at the hands of Cristian Garin and Casper Ruud respectively.

Medvedev, who is still yet to reach the quarters in Madrid, lost the only break of serve in the third game of the opening set but recovered by taking the second set in a tie-break.

Garin dominated the deciding set, the world number 25 breaking Medvedev twice and, after a short delay to fix a broken net, advanced 6-4 6-7 (7-2) 6-1.

Tsitsipas, who held championship point against Nadal in the Barcelona Open final, failed to break Ruud on a single occasion as he fell 7-6 (7-4) 6-4.

Alexander Bublik is next up for Ruud after beating Aslan Karatsev 6-4 6-3, while Matteo Berrettini - 7-6 (7-4) 6-4 winner against Federico Delbonis - will meet Garin.

Also vying for a place in the semi-finals are John Isner and Dominic Thiem, who are set to face off after beating sixth seed Andrey Rublev and Alex de Minaur respectively.

Top seed Stefanos Tsitsipas and fellow star Alexander Zverev progressed to the Mexican Open quarter-finals on Wednesday, but Milos Raonic bowed out.

Tsitsipas was too good for big-serving American John Isner in a 6-3 6-2 victory in Acapulco midweek.

A two-time Australian Open finalist, having also reached the French Open final four last year, Tsitsipas excelled on serve against Isner.

Greek star Tsitsipas only dropped one point on his first serve – not facing a break point throughout the last-16 contest – while firing down eight aces.

Standing in the way of Tsitsipas and a semi-final spot at the ATP 500 tournament is Canadian sensation Felix Auger-Aliassime.

In a battle of the NextGen, seventh seed Auger-Aliassime saved four of five break points in a 6-3 6-4 win over wild card Sebastian Korda.

Zverev will feature in his third Mexican Open quarter-final in four years after the second seed took down Laslo Djere 6-4 6-3.

Runner-up in 2019, Zverev will next face eighth seed Casper Ruud – who topped Tallon Griekspoor 4-6 6-3 7-6 (7-3) in the quarters.

"I think today what showed the most is that I got better with the match," Zverev said. "I started off extremely sloppy, started off with a lot of unforced errors.

"The longer the match went on the better I started playing and this is something that is very important for me. When I get into a rhythm I feel very comfortable on court and that's how I felt today."

Elsewhere, Lorenzo Musetti's giant-slaying run continued following a 2-6 6-3 7-6 (7-1) victory against Frances Tiafoe.

Musetti earned his first ATP 500 quarter-final as the Italian prepares to meet fifth seed Grigor Dimitrov, who eased past Miomir Kecmanovic 6-4 6-2.

There was an upset after fourth seed Raonic crashed out 6-4 6-2 at the hands of Dominik Koepfer, while sixth seed Fabio Fognini lost 6-4 6-3 against Cameron Norrie.