Henin easily disposed of Vania King 6-4, 6-1, capturing her ninth straight match. She has won her last two tournaments in Dubai and Doha to move past Maria Sharapova into the No. 1 spot in the rankings.
Henin will next play Virginie Razzano, who defeated Martina Muller 6-4, 7-6 (7-2).
Clijsters, who won this event two years ago, overcame a first-set loss to defeat Akiko Morigami 4-6, 6-0, 6-0.