INDIAN WELLS, CA, USA -- Naomi Osaka's run through the BNP Paribas Open continued on Friday, as she followed up her first-round victory over Maria Sharapova with a second-round triumph over No.31 seed Agnieszka Radwanska of Poland, 6-3, 6-2.

In the first meeting between the two players, the 20-year-old Japanese player won a whopping 83 percent of points on her first serve throughout the match, and was excellent on return as well, breaking Radwanska four times on eight chances.

"I feel like she plays really good with pace, so I felt like I had to mix it up a lot and just sort of give her a little bit of no rhythm, even though that's what she does to me too," Osaka told the press afterwards. "I was just trying to be mentally really calm and just go for it when I had it."

Osaka will now face either No.3 seed Garbiñe Muguruza from Spain or American qualifier Sachia Vickery in the third round at Indian Wells.

"I'm not really looking out [ahead] too much," said Osaka. "I sort of just want to focus on myself and what I have to do, because I feel like everyone from now -- well, for me, even from the first round is a quality player. I don't want to psych myself out too much."

The players exchanged breaks to start the match, but in the third game, the vaunted Osaka power game began to take hold, as the Japanese player held at love with an ace. Radwanska, to her credit, was initially unfazed, staying on serve through 3-3 with her patented guile and willingness to end points with volleys.

But after racing to a 40-15 lead while serving at 3-4, the Pole hit a few untimely errors to give Osaka a look at a break point, which the 20-year-old converted when a powerful forehand forced a short reply from Radwanska.

Osaka took great confidence from there, and zoomed to triple set point in the next game. A forehand crosscourt winner gave her a love hold and a one-set advantage over the 2014 BNP Paribas Open runner-up. Osaka won an astounding 14 of 15 points on her first serve in the opening set.

Naomi Osaka celebrates during her match against Agnieszka Radwanska. (Getty Images)

Radwanska, a former World No.2 and 2012 Wimbledon runner-up, would continue to fight despite the deficit, and held for 1-0 in the second set after a six-deuce game in which she fended off four break points. But, again, Osaka took a declarative lead at the set's midpoint, breaking for 3-2 behind brutal groundstrokes off both wings.

After breaking Radwanska once more for good measure, Osaka served for the match at 5-2. A crosscourt forehand winner gave the Japanese youngster her first match point, and she had no trouble converting on the first chance, when she followed up a booming serve with a smash at the net to seal victory.

Osaka said her two quality wins make her confident, but she is loath to become "overconfident." The rising star said, "I want to be consistent at this level. I think that's the first thing I want to work on. Other than that, I'm just trying to go, like, one point at a time and one match at a time."