The high biological activity of the chromene compounds coupled with the intriguing optical features of azo chromophores prompted our desire to construct novel derivatives of chromene incorporating azo moieties 4a-l, which have been prepared via a three-component reaction of 1-naphthalenol-4-[(4-ethoxyphenyl) azo], 1, with the benzaldehyde derivatives and malononitrile. The structural identities of the azo-chromene 4a-l were confirmed on the basis of their spectral data and elemental analysis, and a UV–visible study was performed in a Dimethylformamide (DMF) solution for these molecules. Additionally, the antimicrobial activity was investigated against four human pathogens (Gram-positive and Gram-negative bacteria) and four fungi, employing an agar well diffusion method, with their minimum inhibitory concentrations being reported. Molecules 4a, 4g, and 4h were discovered to be more efficacious against Syncephalastrum racemosum (RCMB 05922) in comparison to the reference drugs, while compounds 4b and 4h demonstrated the highest inhibitory activity against Escherichia coli (E. coli) in evaluation against the reference drugs. Moreover, their cytotoxicity was assessed against three different human cell lines, including human colon carcinoma (HCT-116), human hepatocellular carcinoma (HepG-2), and human breast adenocarcinoma (MCF-7) with a selection of molecules illustrating potency against the HCT-116 and MCF-7 cell lines. Furthermore, the molecular modeling results depicted the binding interactions of the synthesized compounds 3b and 3h in the active site of the E. coli DNA gyrase B enzyme with a clear SAR (structure–activity relationship) analysis. Lastly, the density functional theory’s (DFTs) theoretical calculations were performed to quantify the energy levels of the Frontier Molecular Orbitals (FMOs) and their energy gaps, dipole moments, and molecular electrostatic potentials. These data were utilized in the chemical descriptor estimations to confirm the biological activity.