Observational studies of nearby galaxies have demonstrated correlations between the mass of the central supermassive black holes (BHs) and properties of the host galaxies, notably the stellar bulge mass or central stellar velocity dispersion. Motivated by these correlations, the theoretical paradigm has emerged, in which BHs and bulges co-evolve. However, this picture was challenged by observational and theoretical studies, which hinted that the fundamental connection may be between BHs and dark matter halos, and not necessarily with their host galaxies. Based on a study of 3130 elliptical galaxies $-$ selected from the Sloan Digital and ROSAT All Sky Surveys $-$ we demonstrate that the central stellar velocity dispersion exhibits a significantly tighter correlation with the total gravitating mass, traced by the X-ray luminosity of the hot gas, than with the stellar mass. This hints that the central stellar velocity dispersion, and hence the central gravitational potential, may be the fundamental property of elliptical galaxies that is most tightly connected to the larger-scale dark matter halo. Furthermore, using the central stellar velocity dispersion as a surrogate for the BH mass, we find that in elliptical galaxies the inferred BH mass and inferred total gravitating mass within the virial radius (or within five effective radii) can be expressed as $M_{rm{BH}} propto M_{rm tot}^{1.6^{+0.6}_{-0.4}} $ (or $M_{rm{BH}} propto M_{rm{5r_{eff}}}^{1.8^{+0.7}_{-0.6}}$). These results are consistent with a picture in which the BH mass is directly set by the central stellar velocity dispersion, which, in turn, is determined by the total gravitating mass of the system.
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