The world No. 1 player raced past Vliegen 6-1, 6-2, 6-1.
Defending champion Juan Carlos Ferrero of Spain beat Tommy Haas of Germany 3-6, 6-4, 6-4, 6-2 and three-time winner Gustavo Kuerten also advanced.
On the women's side, second-seeded Serena Williams of the United States beat Iveta Benesova of the Czech Republic 6-2, 6-2 and her sister, Venus, seeded fourth, defeated Tamaraine Tanasugarn of Thailand 6-2, 6-4.
Seventh-seeded Jennifer Capriati of the United States won, as did No. 11 Svetlana Kuznetsova of Russia, No. 12 Ali Sugiyama of Japan and former champion Mary Pierce of France.