American Coco Gauff, 19, had to dig deep to get beyond Clara Burel, winning 2-6 6-3 7-6 (7-4) to secure her place in round three.
After taking the opening set, world number 47 Burel led 2-0 in the second before Gauff found her rhythm to break twice and win 6-3.
Gauff, ranked number three in the world, trailed 4-0 and 5-2 in third and final set, but showed grit when winning six of the following eight games to force a tie-break, which she won on the third match point.
“I’m happy with the mental fight,” Gauff told Sky Sports.
“It wasn’t my best tennis. It’s not about how you show up on your good days, it’s about how you show up on bad ones – and I’m happy with how I showed up today.”
The victory is US Open champion Gauff’s 50th WTA 1,000 win, making her the first teenager to achieve that feat just four days before her 20th birthday.
Japan’s Naomi Osaka is among those to join her in the third round after beating Russia’s Liudmila Samsonova, the 14th seed, 7-5 6-3.
Another two seeds were knocked out as American Jessica Pegula, the world number five, was beaten 6-2 3-6 6-3 by Russia’s Anna Blinkova, while China’s Yue Yuan upset compatriot Qinwen Zheng 6-4 6-3.
But Ukraine’s Elina Svitolina, the 16th seed, progressed after beating the Czech Republic’s Katerina Siniakova 6-3 2-6 6-1.
