The fourth-seeded Seles crushed unheralded teenager Maria Sharapova of Russia, 6-0, 6-2. Seles, 28, held the world's top ranking for 178 weeks in the 1990s, while Sharapova will not have a ranking until after this event.
The sixth-seeded Shaughnessy routed Martina Muller of Germany, 6-2, 6-4. Shaughnessy, 22, made quick work of Muller, 19, who was playing for the first time since the second round of the Australian Open.
Both Seles and Shaughnessy received first-round byes and were the only seeds in action Thursday.
Seles is making her sixth appearance here. She lost in the final to Martina Navratilova in 1991 and beat Conchita Martinez for the title in 1992.
Seles has played well of late, winning as the top seed in Doha and reaching the semifinals in Dubai, where she lost to eventual winner Amelie Mauresmo. She is looking for her 53rd career title.
Winners included American Amy Frazier and Anna Smashnova of Israel.
Among those eliminated were Iva Majoli, Kristina Brandi, Paola Suarez, Barbara Rittner and Rachel McQuillan.
Seeded above Seles are Kim Clijsters of Belgium, Hingis and Justine Henin of Belgium.
Clijsters' first foe will be Natalie Dechy of France. Hingis will face Silvia Talaja of Croatia while Henin meets Maja Matevzic of Slovakia.