In this study, novel selective antitumor compounds were synthesized based on their fundamental pharmacophoric prerequisites associated with EGFR inhibitors. A molecular hybridization approach was employed to design and prepare a range of 4H-chromene-3-carboxylates 7a–g, 8, and 11a–e derivatives, each incorporating a sulfonamide moiety. The structures of these hybrid molecules were verified using comprehensive analytical and spectroscopic techniques. During the assessment of the newly synthesized compounds for their anticancer properties against three tumor cell lines (HepG-2, MCF-7, and HCT-116), compounds 7f and 7g displayed remarkable antitumor activity against all tested cell lines, outperforming the reference drug Cisplatin in terms of efficacy. Consequently, these promising candidates were selected for further investigation of their anti-EGFR, hCAII, and MMP-2 potential, which exhibited remarkable effectiveness against EGFR and MMP2 when compared to Sorafenib. Additionally, docking investigations regarding the EGFR binding site were implemented for the targeted derivatives in order to attain better comprehension with respect to the pattern in which binding mechanics occur between the investigated molecules and the active site, which illustrated a higher binding efficacy in comparison with Sorafenib.