Cirstea needed just 1 hour, 16 minutes to dispatch Japan's Ayumi Morita, breezing to a 6-2, 6-2 triumph on the hard courts at Stanford University.
Eighteen-year-old Keys, meanwhile, also moved on with a quick 6-2, 6-2 victory over eighth-seeded Magdalena Rybarikova.
American Nicole Gibbs, Olga Govortsova of Belarus and Switzerland's Stefanie Voegele also logged Day 1 wins.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Texas principal bans speaking Spanish, stirs controversy