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.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys