Former US Open champion Gauff blew a healthy advantage in the second set as Kostyuk sealed a 6-2, 7-5 victory and a third-round meeting with the winner of an all-Polish tie between Magda Linette and Magdalena Frech.

"Coco is an incredible fighter," Kostyuk said. "We always have incredible matches. I tried to stick to what I had to do."

Gauff, playing for the first time since a quarter-final loss to Paula Badosa at the Australian Open on January 21, served seven double-faults and made 39 unforced errors in an erratic display.

The American made a terrible start, slipping 4-1 behind after dropping her serve twice.

Gauff was broken again in the eighth game as Kostyuk secured the first set in just half an hour.

The world number three hit back with a break en route to a 4-2 lead in the second set as she started to find her rhythm.

But Kostyuk battled back, taking advantage of an error-strewn Gauff performance which ended when she served two double-faults to be broken for the fifth time.

"The double-faults made it easier for me... I'm very happy that it ended in two sets," Kostyuk told BeIN Sports.

Rybakina through

Rybakina, who lost to eventual winner Belinda Bencic in the Abu Dhabi semi-finals last week, saw off Payton Stearns in her opening match.

The fifth seed cruised to a 6-2, 6-4 win despite a late wobble to set up a third-round tie against Slovakia's Rebecca Sramkova who beat Russian teenager Mirra Andreeva 3-6, 6-3, 7-5.

Rybakina led 5-0 in the second set but missed three match points to take it 6-0 and then briefly fell apart as Stearns dragged the set back on serve.

The former Wimbledon champion belatedly got over the line on her fifth match point.

Chinese seventh seed Zheng Qinwen joined Gauff in crashing out, though, beaten 6-4, 6-2 by Ons Jabeur.

Three-time Grand Slam finalist Jabeur claimed her first win against a top-10 opponent since last year's Madrid Open after struggling with injury.

The Tunisian will next face 2020 Australian Open champion Sofia Kenin.

Jasmine Paolini, last year's French Open and Wimbledon runner-up, also made a winning start to her campaign with a 6-3, 6-4 victory against Caroline Garcia in the second round.

American sixth seed Jessica Pegula negotiated a tricky second-round match, battling past Elina Svitolina 6-3, 7-6 (7/3).

Czech youngster Linda Noskova earned a last-16 tie against three-time defending champion Iga Swiatek with a 6-2, 6-3 win over Kazakhstan's Yulia Putintseva.

Later, world number one Aryna Sabalenka plays her first match against Russian Ekaterina Alexandrova.