The alkylation of 3,5-dihydro-4H-pyridazino[4,5-b]indole-4-thione with benzyl bromide, ethyl chloroacetate, and allyl bromide in the presence of potassium carbonate (K2CO3) yielded new alkylsulfanylpyridazino[4,5-b]indole derivatives (i.e., compounds 4–6). Hydrazinolysis of ester 6 resulted in hydrazide 7. The structure of compound 6 was verified by X-ray single-crystal analysis. Among the synthesized compounds, compound 6 exhibited the most promising cytotoxicity toward MCF-7 cells with an IC50 value of 12 µM. It showed potential inhibition activity toward EGFR, PI3K, and AKT in MCF-7 cells, with 0.26-, 0.49-, and 0.31-fold reductions in concentration compared to an untreated control. Additionally, it showed apoptosis-inducing activity in MCF-7 cells (47.98-fold); overall apoptosis increased to 38.87% compared to 0.81% in the untreated control, which disrupted the cell cycle at pre-G1 and S phases. Moreover, compound 6 exhibited good binding affinities toward the tested proteins (EGFR, PI3K, and AKT) and had binding energies ranging from −15.87 to −24.87 Kcal/mol. It also formed good interactions with essential amino acids inside the binding sites. Hence, compound 6 is recommended as an anti-breast cancer chemotherapeutic due to its effects on the EGFR-PI3K-AKT pathway.