MORE: Aussie stars lead march in Paris
Maria Sharapova began her French Open defence with a routine first-round win, while 15th seed Venus Williams was dumped out by Sloane Stephens.
Williams, a seven-time major winner but never at Roland Garros, lost out 7-6 (7-5) 6-1 to fellow American Stephens, who proved too strong for her experienced opponent.
Sharapova, who lifted the trophy 12 months ago after defeating Simona Halep in the final, eased past Kaia Kanepi 6-2 6-4 in a professional display.
The Russian will now face Vitalia Diatchenko, who overcame Stefanie Voegele, while Stephens will meet Heather Watson, conqueror of Mathilde Johansson.
Eighth seed Carla Suarez Navarro had little trouble in overcoming Monica Niculescu 6-2 6-2, while Karolina Pliskova - seeded 12th - defeated Zhang Shuai 7-6 (7-4) 6-4.
Other seeds to win on Monday included Sara Errani, Victoria Azarenka, and Angelique Kerber.
Kerber's compatriot Sabine Lisicki ousted Monica Puig 6-2 6-2, while two other Germans in Annika Beck and Carina Witthoeft also advanced, defeating Agnieszka Radwanska and Katerina Siniakova respectively.
There was a mammoth tie-break in the match between Johanna Konta and Denisa Allertova, the latter eventually coming through 7-6 (19-17) 4-6 6-2.
Irina Begu, seeded 30th, progressed 6-4 7-6 (8-6) over Bethanie Mattek-Sands, while there were also straight-sets wins for Sam Stosur, Lucie Hradecka, Elina Svitolina and Ajla Tomljanovic.
Alize Cornet came from a set down to defeat Roberta Vinci, as did Amandine Hesse against Jarmila Gajdosova and Paula Kania in her match with Mona Barthel.
Alexandra Dulgheru saw off Nicole Gibbs 6-3 6-1, and Daria Gavriolva was similarly comfortable in defeating Johanna Larsson 6-1 7-6 (7-3).
Elsewhere, there were wins for Virginie Razzano, Yulia Putintseva, Ana Konjuh, Andreea Mitu and Tsvetana Pironkova.