Herein we report the synthesis of some new 1H-1,2,4-triazole functionalized chromenols (3a–3n) via tandem reactions of 1-(alkyl/aryl)-2-(1H-1,2,4-triazole-1-yl) with salicylic aldehydes and the evaluation of their antifungal activity. In silico prediction of biological activity spectra with computer program PASS indicate that the compounds have a high novelty compared to the known antifungal agents. We did not find any close analog among the over 580,000 pharmaceutical agents in the Cortellis Drug Discovery Intelligence database at the similarity cutoff of 70%. The evaluation of antifungal activity in vitro revealed that the highest activity was exhibited by compound 3k, followed by 3n. Their MIC values for different fungi were 22.1–184.2 and 71.3–199.8 µM, respectively. Twelve from fourteen tested compounds were more active than the reference drugs ketoconazole and bifonazole. The most sensitive fungus appeared to be Trichoderma viride, while Aspergillus fumigatus was the most resistant one. It was found that the presence of the 2-(tert-butyl)-2H-chromen-2-ol substituent on the 4th position of the triazole ring is very beneficial for antifungal activity. Molecular docking studies on C. albicans sterol 14α-demethylase (CYP51) and DNA topoisomerase IV were used to predict the mechanism of antifungal activities. According to the docking results, the inhibition of CYP51 is a putative mechanism of antifungal activity of the novel chromenol derivatives. We also showed that most active compounds have a low cytotoxicity, which allows us to consider them promising antifungal agents for the subsequent testing activity in in vivo assays.