Chromenes are compounds that may be useful for inhibiting topoisomerase and cytochrome, enzymes involved in the growth of cancer and fungal cells, respectively. The aim of this study was to synthesize a series of some novel 2-amino-3-cyano-4-aryl-6,7-methylendioxy-4H-chromenes 4a–o and 2-amino-3-cyano-5,7-dimethoxy-4-aryl-4H-chromenes 6a–h by a three-component reaction, and test these derivatives for anticancer and antifungal activity. Compounds 4a and 4b were more active than cisplatin (9) and topotecan (7) in SK-LU-1 cells, and more active than 9 in PC-3 cells. An evaluation was also made of the series of compounds 4 and 6 as potential antifungal agents against six Candida strains, finding their MIC50 to be less than or equal to that of fluconazole (8). Molecular docking studies are herein reported, for the interaction of 4 and 6 with topoisomerase IB and the active site of CYP51 of Candida spp. Compounds 4a–o and 6a–h interacted in a similar way as 7 with key amino acids of the active site of topoisomerase IB and showed better binding energy than 8 at the active site of CYP51. Hence, 4a–o and 6a–h are good candidates for further research, having demonstrated their dual inhibition of enzymes that participate in the growth of cancer and fungal cells.