Poland's Iga Swiatek, who will become women's world number one after Ashleigh Barty's retirement, earned her 14th straight win by beating Coco Gauff.

Japan's Naomi Osaka also reached the quarter-finals with victory against American Alison Riske.

Last month, Medvedev ended Novak Djokovic's long run at the top of the rankings before the Serb moved back ahead.

But with Djokovic absent in Miami, the 26-year-old Russian will take over again if he reaches the semi-finals.

"I think in general I played not so bad, they are really slow courts here so playing against a Spaniard is not easy," said Medvedev, who has not reached the Miami semi-finals in his previous three main-draw appearances.

"I felt like we had a lot of rallies where he was bringing the pace down in the point and I couldn't do much.

"I tried to serve well, keep consistent and make less errors in the most important points."

Medvedev will next play American world number 39 Jenson Brooksby, who beat Spain's Roberto Bautista Agut.

British number one Cameron Norrie, seeded 10th and the nation's final representative in the draw, will face sixth seed Casper Ruud of Norway in the last 16 on Tuesday.

Greek third seed Stefanos Tsitsipas recorded a 6-4 6-3 win over Australia's Alex de Minaur to set up a last-16 meeting with Spanish teenager Carlos Alcaraz, who beat Croat Marin Cilic 6-4 6-4.

Indian Wells champion Swiatek, 20, continued her quest to complete a rare 'Sunshine Double' - victory in both of the back-to-back tournaments in the United States - with a confident 6-3 6-1 win over 18-year-old American Gauff.

Four-time major champion Osaka, 24, has dropped to 77th in the rankings but, on her favoured hard-court surface, showed further signs of significant improvement in a 6-3 6-4 win over Riske.

Next she will face American ninth seed Danielle Collins, who won 6-2 6-4 against Tunisia's Ons Jabeur.