The evolution of drug resistance in fungal pathogens compromises the efficacy of the limited number of antifungal drugs. Drug combinations have emerged as a powerful strategy to enhance antifungal efficacy and abrogate drug resistance, but the impact on the evolution of drug resistance remains largely unexplored. Targeting the molecular chaperone Hsp90 or its downstream effector, the protein phosphatase calcineurin, abrogates resistance to the most widely deployed antifungals, the azoles, which inhibit ergosterol biosynthesis. Here, we evolved experimental populations of the model yeast Saccharomyces cerevisiae and the leading human fungal pathogen Candida albicans with azole and an inhibitor of Hsp90, geldanamycin, or calcineurin, FK506. To recapitulate a clinical context where Hsp90 or calcineurin inhibitors could be utilized in combination with azoles to render resistant pathogens responsive to treatment, the evolution experiment was initiated with strains that are resistant to azoles in a manner that depends on Hsp90 and calcineurin. Of the 290 lineages initiated, most went extinct, yet 14 evolved resistance to the drug combination. Drug target mutations that conferred resistance to geldanamycin or FK506 were identified and validated in five evolved lineages. Whole-genome sequencing identified mutations in a gene encoding a transcriptional activator of drug efflux pumps, PDR1, and a gene encoding a transcriptional repressor of ergosterol biosynthesis genes, MOT3, that transformed azole resistance of two lineages from dependent on calcineurin to independent of this regulator. Resistance also arose by mutation that truncated the catalytic subunit of calcineurin, and by mutation in LCB1, encoding a sphingolipid biosynthetic enzyme. Genome analysis revealed extensive aneuploidy in four of the C. albicans lineages. Thus, we identify molecular determinants of the transition of azole resistance from calcineurin dependence to independence and establish multiple mechanisms by which resistance to drug combinations evolves, providing a foundation for predicting and preventing the evolution of drug resistance.