In this article, we have designed the new ruthenium(II) p-cymene complexes [Ru(η6-p-cymene) HLThz,MeCl] 1 and [Ru(η6-p-cymene) HLThzCl] 2 with two auxiliary ligand (E)-1-(((5-methylthiazol-2-yl)imino)methyl)naphthalen-2-ol (HLThz,Me) and (E)-1-((thiazol-2-ylimino)methyl)naphthalen-2-ol (HLThz), keeping in mind the vehicle HSA. The spectroscopic techniques, namely, Fourier transform infrared spectroscopy (FT-IR), proton nuclear magnetic resonance (1H NMR), 13C NMR, and elemental analysis were employed for the characterization. The single X-ray crystallography ascertains the molecular structure of the representative complex [Ru(η6-p-cymene) HLThz,MeCl] 1. Furthermore, the density functional theory (DFT) calculation was performed for geometry optimization and frontier molecular orbitals analysis. Moreover, in silico studies were carried out to understand the binding site and the mode of interaction of the complexes with human serum albumin (HSA). The in vitro interaction of the HSA measured extrinsic fluorescence at various temperatures, namely, 298, 303, and 308 K, whereas the intrinsic fluorescence extent was evaluated in the presence of 8-anilinonaphthalene-1-sulfonic acid (ANS). The cytotoxicity of these compounds was evaluated against HeLa, MCF7, HepG2, A549, and A2780 cancer cells and compared with HEK293 non-tumorigenic cells (cisplatin and RAPTA-C as control). The complex 1 showed significantly good cytotoxicity in the range of IC50 value <10 μM against A2780 (ovarian cancer) and HepG2 (liver) cells and lower toxicity up to >100 μM. These findings give illustrative insight into the binding propensity of complexes 1 and 2 with HSA (model protein). Further, they can be explored for en route drug delivery to a specific site as anticancer metallodrugs.