Metallic 1T-phase MoS2 is a promising alternative to platinum-group catalysts for the acidic hydrogen evolution reaction (HER), yet its metastable nature severely limits practical application. Here we present a framework-stabilization strategy for constructing 1T'-phase Mo-Re sulfides by employing the intrinsically distorted 1T' lattice of ReS2 as a structural scaffold. Preferential Mo substitution at Re sites, facilitated by its low formation energy, enables the formation of Re0.5Mo0.5S2 with a high-purity 1T' architecture free of secondary phases. Combined theoretical and experimental investigations reveal that Mo incorporation triggers directional electron transfer and strong Mo 4d/Re 5d/S 3p orbital hybridization, which redistribute charge density, elevate the S 3p band center, and fine-tune the hydrogen adsorption-desorption equilibrium. Consequently, Re0.5Mo0.5S2 achieves exceptional acidic HER performance with a low overpotential of 113 mV at 10 mA cm-2 and remarkable stability exceeding 50 h. This work establishes a versatile paradigm for stabilizing metastable transition metal dichalcogenides, providing new insights into the rational design of metastable functional materials.