Coco Gauff and Naomi Osaka competed at the Silicon Valley Classic. (Carmen Mandato/Getty Images)

Coco Gauff held off a late run from Naomi Osaka to claim a 6-4, 6-4 victory Thursday night at the Silicon Valley Classic.

Osaka fought back after Gauff’s second-set lead extended to 5-1, with the 24-year-old saving seven match points to put the set at 5-4. The 18-year-old American, however, was able to close out the contest on her eighth match point to advance to the tournament’s quarterfinals.

“You know certain players, no matter what the score is, it’s going to be tough. I feel like Naomi is one of those players for me,” Gauff said after the match. “But yeah, at 5-1, 40-0, I was not settled at all. It’s very rare that somebody comes back from 40-0 twice! But you know it’s Naomi, so that shows how much of a fight she has.”

With Thursday’s win, Gauff pulls level with Osaka in the duo’s head-to-head, which now stands at 2-2.

Despite the loss, Osaka appeared in good spirits, taking to Twitter to open up about her mindset.

“I’m really at peace with myself,” Osaks wrote. “I didn’t think I would ever feel like this, it’s kinda fascinating lol.”

Osaka also took time to praise Gauff following their San Jose matchup.

“She’s very much a star. It’s very clear. She’s very important to the game,” Osaka said of Gauff following the match. “After (Roland-Garros) last year when I withdrew, she was the first player to message me and I’ve never forgotten that. I have so much love for her and I think she behaves well beyond her age.”

Gauff will continue on her Silicon Valley Classic run, facing off against No. 4 Paula Badosa in the tournament’s quarterfinal.