There were also wins on Day 3 at Roland Garros for Kvitova, Svitolina and Wozniacki
Simona Halep fights back in delayed match to reach French Open second round
World No 1 Simona Halep battled back after a disastrous opening set to beat Alison Riske 2-6, 6-1, 6-1 in their delayed French Open first-round match on Wednesday, while Petra Kvitova impressed in reaching the third round
Halep, the runner-up in Paris in 2014 and 2017, slumped 0-5 down in the opening set to world No 83 Riske whose only win at the tournament came in 2014.
The Romanian committed 16 unforced errors in the set but stepped up a gear from that point on to book a second-round match against Taylor Townsend of the United States.
"It's always difficult in the first round of a grand slam, you are always nervous," Halep said.
"But I started to run more, played better and kept more balls in play."
The 26-year-old, who is still looking for a first grand slam title, will play for the second straight day today, after the match with Riske was pushed back from Tuesday due to rain.
"I think I'll be ready tomorrow, I feel strong in my legs," the top seed said.
"Anything can happen with the rain so all we can do is rest and try to be at our best when we step on the court."
Halep needs to reach the semi-finals or better if she is to retain the top ranking
Eighth seed Kvitova eased into the third round with a 6-0, 6-4 victory over Spain's Lara Arruabarrena on Court 1.
The two-time Wimbledon champion has now won 13 consecutive matches on clay after claiming titles in Prague and Madrid, and will face Estonia's 25th seed Anett Kontaveit for a place in the last 16.
Czech Kvitova has not reached the quarter-finals at Roland Garros since a run to the last four in 2012.
The 28-year-old raced through the opening set in only 24 minutes, and although she was pegged back after an early break in the second, a booming forehand sealed victory with a third straight game.
Ukrainian fourth seed Elina Svitolina reached the last 32 for the fourth consecutive year by brushing aside Viktoria Kuzmova in straight sets.
The 23-year-old, who arrived in Paris having won her second straight Italian Open title, saw off her Slovakian opponent 6-3, 6-4.
Svitolina, a two-time quarter-finalist at Roland Garros, will take on Romanian 31st seed Mihaela Buzarnescu in the last 32.
Elsewhere, charismatic Japanese 21st seed Naomi Osaka came through a tight match with Kazakhstan's Zarina Diyas 6-4, 7-5.
The 20-year-old Osaka is seeded for the first time at a major tournament, having lifted the prestigious Indian Wells title earlier this year before beating Serena Williams in Miami the following week.
In one of the later matches, second seed Caroline Wozniacki cruised through her second round encounter with Spain's Georgina Garcia-Perez.
The 27-year-old Dane dropped just one game en route to a 6-1, 6-0 victory in just 54 minutes to progress to the last 32.