This work describes the design and synthesis of new hybrids of thienopyrimidine and sulfonamides. The binding affinity of the prepared compounds to FGFR-1 enzyme and caspase-3 was investigated via molecular docking. The cytotoxic effect was estimated for the synthesized compounds against human breast cancer cell lines (MCF-7 and MDA-MB231) using Doxorubicin as a reference. All the tested compounds exhibited moderate to excellent anticancer efficacy against both tested cell lines, among which 3b and 4bi were the best. All the synthesized compounds exhibited distinguishing selectivity index values greater than Doxorubicin. The influence of the new hybrids under inquiry was further examined on both FGFR-1 and Caspase-3. The results revealed that compound 3b showed observed concordance between anti-proliferative activity and Caspase-3 activity. In respect to the compounds’ effect on the apoptosis, compound 3b significantly increased the population of late apoptotic cells and necrotic cells. In silico pharmacokinetic investigation revealed that compound 3b showed the best intestinal absorption, BBB permeability, and, along with 4bi and 4bii, the best CNS penetrability.