"I'm really happy that I could perform so well today," the 29-year-old Safarova said post-game.
Soon after the Safarova-Allertova match completed, Japanese Kurumi Nara joined Safarova at the next stage, sweeping aside German wild card Antonia Lottner 6-2 6-2.
Nara jumped all over Lottner's first serve, converting 64% (18/28) of them into points. She now faces the winner between American Lauren Davis and Dutchwoman Kiki Bertens.
On outside courts at the ASB Tennis Centre, American Jamie Loeb and Czech Barbora Stefkova sealed qualifying spots into the event's main draw.
Loeb defeated fellow American Taylor Townsend 7-6 6-1, while Stefkova accounted for yet another Czech, Tereza Martincova, 6-1 6-3.
Former semi-finalist Mona Barthel of Romania also negotiated her way into the field, defeating Slovenian Dalila Jakupovic 6-2 6-1 in qualifying.
Today's top fixtures will see American top seed Serena Williams take on Pauline Parmentier of France this evening, followed by eighth-seeded Croatian Ana Konjuh v Belgian Kirsten Flipkens.
NZ ace Marina Erakovic and Briton Laura Robson team up against Townsend and Pole Alicja Rosolska in doubles on centrecourt this afternoon.