Top seed Henin, champion here in 2001, beat Germany's Angelique Kerber 6-4, 6-2 as she tunes up for a return to Wimbledon -- the only Grand Slam she has never won -- later in the month.
The Belgian, who returned from retirement at the beginning of 2010, is looking to bounce back from the disappointment of a fourth-round exit at last month's French Open.
She will meet Roberta Vinci for a place in the quarter-finals after the Italian defeated Barbora Zahlavova Strycova of the Czech Republic 6-4, 7-6 (7/5).
There were losses for seeds Sara Errani and Anabel Medina Garrigues, as Italian sixth seed Errani fell 6-1, 6-3 to Austria's Sybille Bammer and Spain's eighth-seeded Medina Garrigues went down 4-6, 6-2, 6-3 to Dutch wild card Arantxa Rus.
Russian third seed Maria Kirilenko was victorious, prevailing 6-4, 6-1 against Romanian Raluca Olaru, while Olaru's fifth-seeded compatriot Alexandra Dulgheru defeated France's Julie Coin 4-6, 7-6 (7/4), 7-6 (7/4).
Former world number one Ana Ivanovic of Serbia will meet German seventh seed Andrea Petkovic in round two thanks to a 4-6, 6-0, 6-1 defeat of Sweden's Sofia Arvidsson.
Dutch sixth seed Thiemo de Bakker was the only major first-round casualty in the men's draw.
He was beaten 4-6, 6-2, 7-6 (7/4) by countryman Igor Sijsling.