Daniil Medvedev celebrated his rise to second in the world with a seamless entry into the Miami Open on Friday, trouncing Taiwan's Lu Yen-Hsun in less than an hour.

Russia's Medvedev needed just 56 minutes to subdue Lu 6-2, 6-2, firing nine aces with just one double fault as he advanced to a third-round meeting with Australian Alexei Popyrin, a 6-4, 6-2, winner over 30th-seeded American Reilly Opelka.

Women's world number two Naomi Osaka, seeded second behind top-ranked Australian Ashleigh Barty, had a tougher time, but conquered her nerves in her first match since winning the Australian Open to beat Aussie Ajla Tomljanovic 7-6 (7/3), 6-4.

"I would say what I'm most proud of today, just being able to handle my nerves," Osaka said.

That was a bigger problem than the gusty wind on Grandstand Court at Hard Rock Stadium, where 77th-ranked Tomljanovic twice went up a break in the opening set but despite an impressive display of power was eventually undone by 24 unforced errors.

Thirteen aces among her 36 winners helped Osaka overcome a slew of unforced errors of her own and set up a third-round meeting with Serbian qualifier Nina Stojanovic, who surprised Yulia Putintseva, the 26th seed from Kazakhstan, 5-7, 7-5, 6-2.

"I served really well when I needed to," Osaka said. "Unfortunately I got broken a couple of times, but I think when it really, really mattered, I was able to serve well, so I'm happy with that.

"I'm happy I was able to get it done in two," Osaka added. "I'm not sure if it was nerves or just I'm a bit rusty but my decision making on some shots was kind of questionable.

"But I think overall I learned as the match was going on."

Medvedev, the top seed in an ATP Masters event for the first time, was all over Lu from the opening game.

He belted 24 winners to become the second player -- along with compatriot Andrey Rublev -- to reach 15 match wins this year.

Runner-up to top-ranked Novak Djokovic at the Australian Open, Medvedev ascended to No. 2 in the world when he lifted the ATP trophy in Marseille.

Medvedev became the first player outside the "Big Four" of Djokovic, Roger Federer, Rafael Nadal and Andy Murray to rank second in the world since Lleyton Hewitt in 2005.

But he's already looking for more.

"The only thing I feel like when you reach something you haven't done then straight away it doesn't matter and you want to go further and further," he said. "I think it's the same for everybody. 

"I'm happy about my achievement but only trying to improve every day and want to go further."

In other action, Australian James Duckworth surprised eighth-seeded Belgian David Goffin 6-3, 6-1 and Britain's Cameron Norrie beat ninth-seeded Bulgarian Grigor Dimitrov 7-5, 7-5.

Canadian 11th seed Felix Auger-Aliassime got past France's Pierre-Hugues Herbert 6-4, 6-4.

"I'm very happy, because it was a tricky first match," said Auger-Aliassime, who split two matches with the Frenchman last year. "I've lost to him before, and I won saving match points. So he's a tricky opponent with a great serve."

Women's sixth seed Karolina Pliskova and No. 12 Garbine Muguruza also advanced in straight sets.

Pliskova beat China's Zheng Saisai 6-2, 6-1 and Spain's Muguruza, coming off a title in Dubai two weeks ago, beat wild card Wang Xinyu of China 6-4, 6-1.