In the present work, we reported the synthesis and characterization [single crystal X-ray diffraction technique, spectroscopic, etc.] of two new Ni(II) and Zn(II) coordination compounds, viz. [Ni(2,6-PDC)2]2[Ni(en)2(H2O)2]2[Ni(en)(H2O)4]·4H2O (1) and [Zn(2,6-PDC)(Hdmpz)2] (2) (where 2,6-PDC = 2,6-pyridinedicarboxylate, en = ethylene-1,2-diamine, and Hdmpz = 3,5-dimethyl pyrazole). Compound 1 is found to crystallize as a multicomponent Ni(II) compound with five discrete complex moieties, whereas compound 2 is isolated as a mononuclear Zn(II) compound. A deep analysis of the crystal structure of 1 unfolds unusual dual enclathration of guest complex cationic moieties within the supramolecular host cavity stabilized by anion–π, π-stacking, N–H⋯O, C–H⋯O, and O–H⋯O hydrogen bonding interactions. Again, the crystal structure of compound 2 is stabilized by the presence of unconventional C–H⋯π(chelate ring) interactions along with C–H⋯O, C–H⋯N hydrogen bonding, π-stacking, and C–H⋯π(pyridyl) interactions. These non-covalent interactions were further studied theoretically using density functional theory (DFT) calculations, molecular electrostatic potential (MEP) surfaces, non-covalent interaction (NCI) plot index, and quantum theory of atoms in molecules (QTAIM) computational tools. The computational study displays that π-stacking or H bonds greatly tune the directionality of compound 1, although non-directional electrostatic forces dominate energetically. For compound 2, a combined QTAIM/NCI plot analysis confirms the presence of unconventional C–H⋯π(chelate ring) interactions along with other weak interactions obtained from the crystal structure analysis. Further, the individual energy contributions of these weak yet significant non-covalent interactions have also been determined computationally.