Updated

Paris, France (SportsNetwork.com) - World No. 1 superstar Serena Williams, fourth-seeded Petra Kvitova and fifth seed Caroline Wozniacki notched opening- round wins, while struggling Canadian star Genie Bouchard was shown the door Tuesday at the 2015 French Open.

Williams waltzed past Czech Andrea Hlavackova 6-2, 6-3 in less than an hour to improve to a stellar 26-1 this year and 58-1 in her career first-round Grand Slam matches.

The 33-year-old American is going for her 20th Grand Slam singles title. Only two women have won more -- Margaret Smith Court (24) and Steffi Graf (22).

The reigning Australian and U.S. Open titlist Williams is a two-time French Open champ (2002, 2013). Her second-round opponent will be German Anna-Lena Friedsam.

The Wimbledon champion and recent Madrid titlist Kvitova gutted out a 6-4, 3-6, 6-4 win over New Zealand's Marina Erakovic, while the U.S. Open runner-up Wozniacki waltzed past last week's Nurnberg clay-court champ Karin Knapp of Italy 6-3, 6-0.

And inspired Frenchwoman Kristina Mladenovic erased the sixth-seeded Bouchard 6-4, 6-4. Mladenovic was a clay-court runner-up in Strasbourg, France, last week.

All of Mladenovic's previous Top-10 wins also come in Paris -- Kvitova (Paris Indoors 2013), Simona Halep (Paris Indoors last year) and, Li Na (last year at the French Open).

Mladenovic was asked afterwards about all of those Top-10 wins coming in her nation's capital.

"Well, thank you for asking. I don't really know. I wasn't even aware of that statistic," she said. "I remember I've played good matches against good players elsewhere, but it's even more special to be playing at Roland Garros. You get more satisfaction from it. It's more difficult, mentally, to manage the pressure here, because people expect so much from us. But I think I know how to manage that pressure."

The 2014 Wimbledon runner-up Bouchard, who reached at least the quarterfinals in four of the previous five majors, has been playing poorly since appearing in the Australian Open quarters back in January.

"About today, I mean, honestly, I don't know what to say," Bouchard said. "I felt I was in the match. But tennis-wise, I still knew I was far off from how well I can play. But, you know, I was in there. It's been kind of the same as how I have been feeling recently on the court. Just not like myself.

"I have been trying to work on what's been going wrong, and I feel like I've been making progress, so to still have matches like this is disappointing. But at the same time it's just a tennis match -- life is still good, everyone has highs and lows in their careers, and this is just a little bit of a low point for me."

A French Open semifinalist a year ago, Bouchard is 7-10 overall this season, including five tournament-opening losses.

One of this year's Aussie Open semifinalists, 16th-seeded American Madison Keys, avoided an upset by topping fellow countrywoman Varvara Lepchenko 7-6 (7-3), 6-3.

Meanwhile, 10th-seeded German Andrea Petkovic whipped American Shelby Rogers 6-2, 6-1 and 18th-seeded Russian Svetlana Kuznetsova held off Dutchwoman Kiki Bertens 6-1, 4-6, 6-2. The two-time Grand Slam winner Kuznetsova was the French Open champion in 2009 and runner-up in 2006.

Bulgaria's Sesil Karatantcheva posted an upset by taking out 25th-seeded former world No. 1 Jelena Jankovic 6-3, 6-4. The former U.S. Open runner-up Jankovic is a three-time French Open semifinalist, but hasn't reached the final four here since 2010.

Also on Day 3, 23rd-seeded rising Swiss Timea Bacsinszky handled Spaniard Lara Arruabarrena 6-3, 6-4 and 32nd-seeded Zarina Diyas of Kazakhstan doused German Dinah Pfizenmaier 6-4, 6-1.

Several other women reached the second round, including former French Open champion Francesca Schiavone of Italy, Swiss Belinda Bencic, American Irina Falconi and German Julia Goerges.

Wednesday's schedule will feature 16 women's second-round matches, highlighted by ones for second-seeded Maria Sharapova, third-seeded Simona Halep and seventh-seeded Ana Ivanovic.

The former world No. 1 and reigning French Open champion Sharapova will meet fellow Russian Vitalia Diatchenko, while the 2014 French Open runner-up Halep will battle Croat Mirjana Lucic-Baroni and the former top-ranked star Ivanovic will be opposed by Japan's Misaki Doi.

The 2015 Aussie Open runner-up Sharapova is a five-time Grand Slam champion, including French Open titles in 2012 and last year. She was the 2013 runner-up to Williams and is seeking a trip into a fourth straight final in Paris. Ivanovic captured the Roland Garros title in 2008 and was the runner-up in 2007.