For the fourth time overall and third on U.S. hard courts, Coco Gauff and Naomi Osaka will go head-to-head -- this time at the Mubadala Silicon Valley Classic.

Gauff followed Osaka through to Round 2 on Tuesday night with a 6-1, 6-0 win over Ukraine's Anhelina Kalinina that lasted just 55 minutes. 

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Here are three takeaways from Gauff's opening victory in her San Jose debut that earned her another meeting with four-time Grand Slam champion Osaka.

San Jose: Gauff puts on hot shot show to win opener

Gauff on cruise control: The sixth-seeded American, ranked a career-high No. 11 this week, set the tone early against Kalinina. She lost three points in the first three games, and the bar stayed high. In fact, she didn't face a break point until her fifth service game, already with a one-set lead.

Gauff hit 12 winners to Kalinina's one in the opener, and the trend continued in the second set. In all, the American hit 29 winners to 14 unforced errors in the match and broke serve five times. She also served seven aces. 

All of the lights, under the lights: After the match, Gauff couldn't have been more pleased with her performance -- and her spot on the schedule.

"Today's match was great," she said. "I was glad to find out I was playing the night match. I love night sessions. ... This crowd was pretty energetic. It's a small stadium, but the sound is really loud, so I enjoyed it."

Even with growing accolades, Coco Gauff taking nothing for granted

She'll get another chance to play under the lights on the campus of San Jose State University against Osaka. Their Round 2 match will be played on Thursday evening.

Previewing Gauff vs. Osaka: Osaka owns a 2-1 head-to-head record against Gauff. The pair famously played in the third round of the US Open in 2019, where Osaka comforted a teary-eyed Gauff after a 6-3, 6-0 win in a moment of sportsmanship heard around the world. Their second meeting was also a straight-setter but won by Gauff in Round 3 of the 2020 Australian Open -- where Osaka was the defending champion.

Their last meeting though? The most competitive. Last summer in Cincinnati, Gauff won the opening set against second-seeded Osaka at the Western & Southern Open before Osaka rallied for a 4-6, 6-3, 6-4 win.

"I played her a lot of times and she's obviously going to be a tough opponent," Gauff said. "Either way, win or lose, I think that the match is going to be great. She's such a champion, on and off the court, so I guess those are the type of people that you want to play, and I look forward to playing those matches." 

Osaka was similarly complementary of Gauff.

"What's always impressed me about Coco is her mentality," Osaka said. "When I was her age, I would find myself getting frustrated and I would show it. I just think it's really cool how she's able to stay really neutral all the time.

"She's been on the tour for a while and I think people don't know that because of how young she is. She's improving every year, so I think there's a lot that she's learning and it's only a matter of time before she wins a [Grand] Slam.

"The last time we played in Cincy, I was just really tense there. ... I'm just looking to see what she's improved. When I go on the court, I know who I am, so I just want to see what she's going to bring."