SAN JOSE, Calif. -- No.11 Coco Gauff defeated former No.1 Naomi Osaka 6-4, 6-4 to advance to the quarterfinals of the Mubadala Silicon Valley Classic on Thursday night. The victory leveled Gauff's career head-to-head against Osaka to two wins apiece. She will face No.2 seed Paula Badosa on Friday.

Gauff's serve proved the difference: Facing one of the best servers on tour, Gauff dominated on her service games. The serve has been clicking for the American in San Jose. In her near-perfect match in the opening round against Anhelina Kalinina she won 89.3% of her first serve points, her highest mark of the last two seasons. 

That trend continued against Osaka, who was unable to generate a single break point on the youngster's serve until late in the match. Just one break of serve separated the two through the first set, but Gauff kept the pressure on Osaka in the second to break her twice and build a 5-1 lead. 

Osaka's champion's mettle took over late in the second set, as she saved four match points from 0-40 to hold to 5-2. Osaka then broke Gauff for the first time in the match, as the American played her first tight game of the night. 

Serving again to stay in the match, Osaka fell behind 0-40 and saved all three match points to bring her total tally to seven. Osaka hold serve with a roar to force Gauff to serve out the win for a second time at 5-4. 

"When I was playing the match just now I realized that I've been letting people call me mentally weak for so long that I forgot who I was," Osaka said. "I realized that that's something that I do. I lost the match today but I feel really confident in who I am. I feel like the pressure doesn't beat me. I am the pressure. I'm really happy with that."

This time Gauff did not falter, closing out a dramatic finish on her eighth match point with an unreturnable body serve. 

"At 5-1, 0-40 I was not settled at all," Gauff said. "It's very rare that someone comes back from 0-40 twice but it's Naomi. That just shows how much of a fight she has. She could have easily thrown in the towel but she didn't."

Osaka struggled to hit through Gauff's baseline defense: Gauff's movement is second to none, but Osaka has successfully found holes in her game in her two prior wins at the 2019 US Open and their last meeting in Cincinnati last summer. That was not the case on a mild night in San Jose. As the sun set the conditions clearly began to favor the speedy American. She held Osaka to just 12 winners in the match while unleashing on her own strokes, striking 19 winners. 

"I think I improved in all aspects and today showed it," Gauff said. "I knew playing Naomi was going to be tough. I think she has one of the best baseline games in the game. When I play her I know that if she does win the match that's where she's going to get me, in those baseline rallies. I think today I really held my ground and winning a lot more of those rallies than she was. That just shows how much I'm improving. The last three weeks, so many hours on the court and I'm glad it's coming together."

This was the best of their four meetings: Nerves played a part in their prior three matches. Gauff was overwhelmed by the moment in their memorable first encounter in New York and Osaka was nervy in their second a few months later at the Australian Open. Osaka edged Gauff in three sets last summer in Cincinnati, but the former No.1 acknowledged being incredibly tight throughout that scratchy affair.

Nerves played no role on Thursday night. It was an accurate reflection of their respective games at the moment. Between her dominating serve and steady forehand, San Jose has been a fantastic showcase for all the improvements in Gauff's game this year. Having made her maiden major final at the French Open, Gauff is now knocking on the door of the Top 10, with no one questioning her right to the milestone. 

Despite the heavy scoreline, this was by no means a poor performance from Osaka, who showed her class in the first round to beat Zheng Qinwen in three quality sets. Against Gauff she rediscovered her fighting grit and leaves San Jose in good spirits while acknowledging the need for matches.

But there's a reason Gauff sits at No.3 behind Iga Swiatek and Ons Jabeur in the Porsche Race to the WTA Finals Leaderboard. The 18-year-old has been one of the best players in the world in 2022. On this night, she showed precisely why. 

San Jose: Gauff beats Osaka to level head-to-head, into QFs