Sugiyama will face Slovakia's Dominika Cibulkova , a 6-2 6-3 second-round winner over Ukraine's Kateryna Bondarenko.
Germany's Sabine Lisicki and Russia's Svetlana Kuznetsova were also winners, beating Dominika Cibulkova and Nadia Petrova respectively.
The sixth-seeded Australian, who was runner-up in Paris in 2010, will next face Azarenka's conqueror Dominika Cibulkova.
Li, returning to her best form on clay, was rarely troubled by Dominika Cibulkova of Slovakia, winning 6-1 7-6.
In the women's section, Serena Williams thrashed Slovakia's 14th seed Dominika Cibulkova 6-0 6-1 to make it 21 consecutive victories.
The Russian, who upset French Open champion Svetlana Kuznetsova in the second round, progressed after beating Slovakia's Dominika Cibulkova 4-6 6-1 6-1.
The Australian Open runner-up will next play Slovakian 26th seed Dominika Cibulkova.
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In the Barcelona Open, Italy's seventh seed Sara Errani shocked third seed Dominika Cibulkova of Slovakia 6-2 6-2 to win the clay court event.
Fourth-ranked Agnieszka Radwanska sent out a warning to the top three by thrashing Dominika Cibulkova 6-0 6-0 in Friday's final of the Sydney International.
Russian qualifier Valeria Savinykh upset No. 15 Dominika Cibulkova 7-6 (6), 6-4 and Kirsten Flipkens of Belgium beat No. 23 Klara Zakopalova 6-1, 6-0.
Ekaterina Makarova and Elena Vesnina won the deciding doubles rubber, beating Dominika Cibulkova and Daniela Hantuchova 4-6 6-3 6-1 in two and a half hours.
Third seed Daniela Hantuchova cruised past unseeded Slovakian compatriot Dominika Cibulkova 6-1 6-4 and will now play 13th seed Sybille Bammer, who beat Karolina Sprem 6-2 6-3.
Radwanska will face the tournament's surprise package Dominika Cibulkova in the final after the Czech world No. 15 beat German second seed Angelique Kerber 6-2 4-6 6-3.
Serbia, beaten in last year's final, received a lifeline when Slovakia's Dominika Cibulkova retired due to severe cramps when leading 6-4 5-4 against Vesna Dolonc in Nis.
Slovakia's Dominika Cibulkova, who is seeded a lowly 26th despite reaching the last four here in 2009, is also safely through after beating Russia's Ekaterina Ivanova 6-2 6-0.
Top seed Caroline Wozniacki defeated Slovakia's Dominika Cibulkova 6-2 7-6 (7-2) and the Danish world No. 3 will play Israel's Shahar Peer for a place in the quarterfinals.
The 20-year-old, who is playing her first Grand Slam as world number one, will face Slovakian Dominika Cibulkova , who beat Italy's Alberta Brianti 6-1 4-6 6-2, in the next round.
Dominika Cibulkova beat Anastasia Pavlyuchenkova 5-7 6-1 6-4, and then Daniela Hantuchova defeated Maria Kirilenko 6-2 6-4 as the Slovakians seek to reach their first final since winning the 2002 title.
Seeds Agnieszka Radwanska, Flavia Pennetta, Alisa Kleybanova, Agnes Szavay, Sybille Bammer and Aleksandra Wozniak also advanced, but Alize Cornet, Dominika Cibulkova, Zheng Jie, Ai Sugiyama and Sara Errani failed to progress.
The Belgian was joined in the next round by compatriot and wildcard Justine Henin, although the former world number one was made to battle a bit harder before edging past Dominika Cibulkova 6-4 6-4.
Petrova won her first-round tie against compatriot Elena Vesnina, triumphing 4-6 6-2 6-3, while Chinese 13th seed Li Na beat Spain's Beatriz Garcia Vidagany 6-0 6-2 to set up a clash with Slovakia's Dominika Cibulkova.
The Australian Open champion trailed 6-1 4-0 against Dominika Cibulkova before defeating the Slovakian 16th seed in three sets -- their last five meetings have gone the distance, with Azarenka winning four to be 7-1 overall.
Williams, who next plays 26th seed Dominika Cibulkova after she came from a set down to beat Varvara Lepchenko, has never won the French Open and in 13 previous appearances, her best finish was a final place in 2002 when she lost to sister Serena.
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