Rezai, who came into the tournament unseeded, slipped past Uzbekistan's Akgul Amanmuradova 6-2, 4-6, 6-3 to advance to the round of 16.
Rezai of France bested Argentine Gisela Dulko in last year's Bastad finale.
Russian Vesna Dolonts, meanwhile, stunned Safarova of the Czech Republic, 6-3, 6-4.
Also Monday, fourth-seeded Spaniard Lourdes Dominguez Lino defeated Swedish wild card Ellen Allgurin 6-3, 6-4 and No. 7 Barbora Zahlavova Strycova of the Czech Republic dispatched Swedish wild card Hilda Melander 6-2, 6-3.
Top-seeded Caroline Wozniacki, the world's top-ranked player, is set to meet France's Alize Cornet in her opener.
Notable deaths of 2014 [PHOTOS]