Coco Gauff overcame 13 double-faults on Wednesday as she battled past Wimbledon champion Elena Rybakina and into the third round of the WTA Toronto Masters, where top-ranked Iga Swiatek sailed through.

Gauff, the US teenager who fell to Swiatek in the French Open final this year, held on to beat Rybakina 6-4, 6-7 (8/10), 7-6 (7/3).

Gauff lost out on four chances to close out a straight-sets victory as a quartet of match points came and went.

Kazakhstan's Rybakina, aided by Gauff's service struggles, had looked as if she might pull off another marathon victory. She had needed three hours to get past Marie Bouzkova in the first round.

But Gauff finally prevailed, 70 minutes after her first opportunities, claiming victory on her fifth match point.

Both players were appearing for the first time in Francophone Montreal after making Canadian debuts a year ago in Toronto.

World number 11 Gauff lost serve three times against Rybakina but broke on four occasions.

Meanwhile, Swiatek glided through untroubled in her second-round match, defeating Australian Ajla Tomljanovic 6-1, 6-2 in 55 minutes.

The top-seeded Pole with six titles this season faced nine break points, saving six.

"From the first practice I played here I felt really good," Swiatek said.

"Even though there was jet lag and I was coming from clay I felt like I was in a good place. "It's this whole tournament and city that is giving me that, I really like being here."

Swiatek was playing her second tournament since losing to Alize Cornet in the third round at Wimbledon last month, a defeat which ended her 37-match win streak.

"I'm pretty happy I could actually just play my game. It was the first match so it's never easy," she said.

"But I feel like I found my rhythm; it was a pretty solid performance."

Defending champion Camila Giorgi made it to the third round with a 6-3, 7-5 defeat of Belgian Elise Mertens.

Spanish fourth seed Paula Badosa lasted for just 13 games before retiring as she trailed 7-5, 1-0 against Kazakh Yulia Putintseva.

Simona Halep beat Zhang Shuai of China 6-4, 6-2.