We have described a simple, convenient, and high-yielding one-pot synthesis of novel azo chromene derivatives via a three-component reaction of various azo aldehydes with dimedone and malononitrile using 10 mol% of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) as catalyst and ethanol as solvent at reflux condition. All the synthesized compounds have been characterized using Fourier-transform infrared spectroscopy (FT-IR), 1 H NMR, 13 C NMR, and HR-MS spectra and molecular docking was performed to explore new inhibitors of human placental aromatase cytochrome P450 and cyclooxygenase-2 enzymes. Of all the compounds docked, compound (E)-2-amino-4-(4,4-dimethyl-2,6-dioxocyclohexyl)-6-((3-methoxyphenyl)diazenyl-4H-chromene-3-carbonitrile (4o) showed good binding affinity with the active site of human placental aromatase cytochrome P450 enzyme (PDB: 3EQM) with inhibition constant (Ki) 1.66 nM and compound 4o also showed good binding affinity with the active site of cyclooxygenase-2 enzyme (PDB: 6COX) with inhibition constant (Ki) 367.17 pM. In vitro anti-cancer activity studies against MCF-7 cells were also performed for compounds 4o, anastrozole and celecoxib. Compound 4o showed an effective cytotoxicity at 19.8 μg/ml compared to anastrozole and celecoxib (24.7 and 26.2 μg/ml).