Chlorogenic acid (CHA) and gallic acid (GA) are safe natural phenolic compounds that are used as enhancers of some drugs in influencing antioxidant, anticancer, and antibacterial activities. Among fungi, Candida spp. and Malassezia spp. are characterized by an increasing prevalence of multidrug resistance phenomena and by a high morbidity and mortality of their infections. No data are available about the efficacy of CHA and GA combined with azoles on the antifungal susceptibility and on the virulence of both fungi. Therefore, their antifungal and antivirulence effects have been tested in combination with fluconazole (FLZ) or ketoconazole (KTZ) on 23 Candida spp. and 8 M. furfur isolates. Broth microdilution chequerboard, time-kill studies, and extracellular enzymes (phospholipase and hemolytic) activities were evaluated, displaying a synergistic antifungal action between CHA or GA and FLZ or KTZ on C. albicans, C. bovina, and C. parapsilosis, and antagonistic antifungal effects on M. furfur and Pichia kudriavzevii (Candida krusei) isolates. The time-kill studies confirmed the chequerboard findings, showing fungicidal inhibitory effect only when the GA was combined with azoles on Candida strains. However, the combination of phenolics with azoles had no effect on the virulence of the tested isolates. Our study indicates that the combination between natural products and conventional drugs could be an efficient strategy for combating azole resistance and for controlling fungistatic effects of azole drugs.