The reaction of K2[PtCl4] and K2[PtCl6] with 5-methyl-5-(2-pyridyl)-2,4-imidazolidenedione (L) proceeded with the deprotonation of L forming Pt(II) and Pt(IV) complexes, K[PtCl2(N,N-L)] (1) and K[PtCl4(N,N-L)] (2), respectively. Within several weeks in DMSO/CH3OH solution of both complexes 1 and 2 the crystalline platinum(II) complex, PtCl(N,N-L)(DMSO) (3), was obtained, corresponded to a substitution reaction (on 1 and 2) and unanticipated reduction (on 2). The nature of the reducing agent is unknown. Single crystal X-ray diffraction analysis proved bidentate N-coordinated fashion and square planar arrangement for L and 3, respectively. The quantum chemical calculations supported the crystal packing findings in which intermolecular classical and non-classical hydrogen bonds was found. The reaction of L with K2[PdCl4] and PdCl2 gave the same complex of palladium(II) with 2:1 ligand–metal ratio, Pd(N,N-L)2 (4). DFT studies showed the intramolecular hydrogen bonding has significant effect on the stabilization of trans isomer for this complex. Antibacterial studies against six bacterial strains showed main compounds L, 3, and 4 represent activity with low levels of inhibitory potency. In vitro cytotoxicity studies in MCF-7 and A-549 tumor cell lines on 3 were in accordance with the reported data, the substitution of one chlorido ligand with DMSO molecule highly inactivates in vitro antitumor activity.