NEW YORK (Reuters) -American third seed Coco Gauff completed a confidence-boosting 6-3 6-1 win over Poland's Magdalena Frech in the U.S. Open third round on Saturday, finding her rhythm after a nervous start to the tournament.

Gauff made a flurry of unforced errors in her opening match and struggled with her serve in a tearful second-round win, but the 2023 champion kept her cool to subdue the 28th seed and set up a blockbuster fourth round showdown with another Flushing Meadows fan favourite -- twice winner Naomi Osaka.

"I have been on this tour since I was 15, and I think I've done pretty well with the mental side of things," she said.

"There are moments I wish I could show up better, but when they happen, I think I just try to get up and be a better version of myself. Well, sometimes the next point, not even the next day."

After trading early breaks, Gauff broke the Pole in the eighth game and pumped her fist in celebration as Frech sent a shot out on set point.

The Roland Garros winner showed considerable improvements on her much-maligned serve, with four double faults compared to 18 across her first two rounds, and outlasted Frech in a 20-shot rally to get the break in the third game of the second set.

Gauff broke her to love in the fifth as the unseeded Pole made a number of unforced errors and was firing on all cylinders from the baseline in the final game as Frech sent another shot out on match point.

"It's been an emotional week," said Gauff, who booked her fourth straight trip to the Flushing Meadows round of 16.

"I think I needed those tough moments to be able to move forward. I was putting so much pressure on myself."

(Reporting by Amy Tennery in New York, editing by Ed Osmond and Pritha Sarkar)