Aspergillus parasiticus and Aspergillus ochraceus are important pathogenic fungi that pose a serious threat because of their ability to produce mycotoxins, including ochratoxin A (OTA) and aflatoxins (AFs). The main method of reducing these pathogens is the use of chemical fungicides, though recently there has been a focus on finding biological control agents. The obtained results from this study indicate the great potential of two wild yeast strains, Aureobasidium pullulans PP3 and Saitozyma podzolicus D10, in the biological control of A. parasiticus and A. ochraceus and reductions in the amount of OTA and AFs they produce. In vitro, the growth of the mycelium of pathogens was reduced by 41.21% to 53.64%, and spore germination was inhibited by 58.39% to 71.22%. Both yeast strains produced the enzymes chitinase, β-1,3-glucanase, and amylase, and A. pullulans PP3 additionally produced protease and cellulase. This yeast strain also had the ability to grow over a wide range of temperature (4–30 °C), salinity (0–12%) and pH (4–11) conditions. No growth of the yeast was observed at 37 °C, nor any biogenic amines or hydrogen sulfide production. Adding the tested yeast inoculum to the dough reduced OTA (within 14.55–21.80%) and AFs (within 18.10–25.02%) in the model bread.