Daniil Medvedev moved to within two wins of reclaiming the ATP's No 1 ranking after easing past Pedro Martinez 6-3, 6-4 on Monday to reach the last 16 at the Miami Open, while Naomi Osaka cruised into the quarter-finals of the women's draw.
Medvedev, who will replace Novak Djokovic at the top of the rankings if he reaches the Miami semi-finals, fired down 14 aces and broke Martinez three times to secure victory in 84 minutes.
"I just felt like I had to be more consistent, and the more consistent one today would win," Medvedev said. "I managed to just make a few less errors at important moments, serve even better, and it was a small margin but I managed to win and I'm really happy."
Up next for the Russian, who lost the No 1 ranking after a surprise third-round loss at Indian Wells, will be American Jenson Brooksby, who defeated Spain's Roberto Bautista Agut 6-3, 5-7, 6-4.
Spanish 14th seed Carlos Alcaraz will meet Stefanos Tsitsipas after both enjoyed straight-set wins over Marin Cilic and Alex de Minaur respectively.
Alcaraz, 18, beat world No 5 Tsitsipas in their only previous meeting, a five-set thriller at last year's U.S. Open.
"He is a great player," the Greek third seed said of Alcaraz. "For me it will be a great challenge, the ones that I like."
Indian Wells champion Taylor Fritz dispatched fellow American Tommy Paul 7-6, 6-4 and will meet Serbian Miomir Kecmanovic, a 7-6, 6-3 winner over Sebastian Korda.
Fritz said it is all about managing expectations having battled through an ankle injury to win the Indian Wells title.
"I didn't really think about winning Indian Wells until I had match point in the final," he said. "So I'm approaching this one the same way. I don't expect to win the tournament, but I take it one match at a time, and you never know."
'Grateful' Osaka in fine form
Japan's Osaka reached the quarter-finals for a second consecutive year with a 6-3, 6-4 win over American Alison Riske, recovering after falling behind 2-0 in the second set.
After the match, the unseeded Osaka said she was in a different state of mind than last year when arriving at the Miami Open after winning the Australian Open.
"It's really funny for me because last year I made it to the (Miami) quarters too but it was after I won Australia and I wasn't that grateful, I kind of expected to win," said former world No 1 Osaka, who has slipped to No 77 in the rankings.
"But I'm in the same position this year so this is really like one of the funnest times of my life."
Standing between the four-time Grand Slam champion and a first Miami semi-final will be Australian Open finalist Danielle Collins, who beat Tunisian eighth seed Ons Jabeur 6-2, 6-4.
Poland's new world No 1 Iga Swiatek eased past 14th seed Coco Gauff 6-3, 6-1 and will next face Petra Kvitova after the Czech defeated Veronika Kudermatova 7-6, 6-4. Swiatek is aiming to complete the rare 'sunshine double' having claimed the Indian Wells title in California last week.
Spanish fifth seed Paula Badosa beat 16-year-old wildcard Linda Fruhvirtova 6-2, 6-3 and will next meet Jessica Pegula, who reached the Miami quarter-finals for the first time after Anhelina Kalinina retired while trailing 6-0.
Badosa, who won the Sydney title this year and reached the semis at Indian Wells, told reporters it had been a tough day.
"I didn't wake up feeling well so I didn't know if I'd be able to finish the match," she said. "I always say I want to be a fighter no matter what so that's what I did. I kept fighting and I don't really know how I won."