In this study, we synthesized novel sulfonamides with a 1,2,4-triazine moiety according to pharmacophore requirements for biological activity. All the synthesized compounds were tested in vitro to verify whether they exhibited anticancer activity against the human breast cancer cell lines MCF-7 and MDA-MB-231. Among them, two most active ones, having IC50 values of 50 and 42 µM, respectively, were found to show higher anticancer activity than chlorambucil used as the reference in the in vitro tests. In addition, two other compounds, which had IC50 values of 78 and 91 µM, respectively, exhibited a similar level of activity as chlorambucil. X-ray analysis carried out for two of the compounds confirmed their synthesis pathway as well as their assumed molecular structures. Furthermore, a conformational analysis was performed, and electronic parameters of molecules were characterized using theoretical calculations at AM1 and DFT level. Moreover, molecular docking revealed the mode of binding of the investigated 1,2,4-triazine sulfonamides with the human estrogen receptor alpha (ERα).