Mauresmo, the tourney's defending champion and former world No. 1, ousted Perry 6-3, 6-4 in straight sets while Williams, the 2003 and 2004 Aussie Open champion, rolled over Santangelo, 6-2, 6-1 at Rod Laver Arena in Melbourne.
Mauresmo meets Russia's Olga Poutchkova and Williams plays Anne Kremer of Luxembourg in their second-round matches.
In other first-round action Monday, third-seeded Svetlana Kuznetsova of Russia swept Australia's Jessica Moore, 6-2, 6-0; fifth-seed Nadia Petrova of Russia slammed Tamarine Tanasugarn of Thailand, 6-3, 6-2; and No. 7 Elena Dementieva of Russia downed Stephanie Foretz of Spain, 6-1, 6-2.