Quantum droplets (QDs) represent a unique class of self-bound ultracold atomic clusters that can stably persist in dilute atomic quantum gas systems without relying on external trapping potentials, and their stability is fundamentally governed by the delicate balance between conventional mean-field inter-atomic interactions and quantum fluctuation corrections originating from the Lee-Huang-Yang (LHY) effect. Despite substantial progress in the theoretical and experimental exploration of QDs physics, most existing theoretical models and equation of state (EOS) descriptions commonly adopt a simplified approximation that neglects anisotropic p-wave atomic interactions. In ultracold binary bosonic mixtures, such anisotropic short-range interactions are capable of strongly amplifying quantum fluctuation effects, fundamentally breaking the conventional mean-field-LHY balance condition and qualitatively modifying the intrinsic stabilization mechanism, structural properties, and dynamic behaviors of self-bound QDs. To address this critical research gap, this work systematically investigates the physical impacts of anisotropic p-wave interactions on the equilibrium properties and stabilization mechanism of three-dimensional (3D) binary bosonic QDs, with a focus on revealing the novel quantum effects induced by anisotropic higherorder interactions. We establish a zero-temperature self-consistent effective field theory framework that fully incorporates anisotropic p-wave interaction terms, and analytically derive the modified EOS for 3D binary bosonic mixtures. By implementing the Hubbard-Stratonovich (HS) transformation to decouple the complex interaction terms, we theoretically verify that interspecies attractive interactions in the system can induce robust nonperturbative bosonic pairing, which is quantitatively characterized by the pairing order parameter Δ. The formation of bosonic pairs further remodels the traditional LHY quantum fluctuation terms, yielding a series of non-universal modified LHY corrections that inherently carry the short-range spatial and anisotropic characteristics of p-wave interactions. Notably, the proposed modified theoretical model can perfectly reproduce the classic universal EOS of conventional QDs in the zero-range interaction limit, which demonstrates the consistency and reliability of our extended theory. Compared with traditional mean-field theoretical frameworks, our improved model effectively compensates for the deficiency of neglecting anisotropic higher-order interactions, accurately clarifying the quantitative correlation between p-wave interaction strength, bosonic pairing behavior, and QDs stabilization. The findings of this work provide a comprehensive and rigorous theoretical understanding of anisotropic higher-order interaction effects in ultracold bosonic quantum gases, fill the theoretical blank of p-wave dominated QDs modulation mechanisms, and lay a solid theoretical foundation for the subsequent experimental observation of anisotropic QDs states and the exploration of exotic emergent quantum phases in multi-component ultracold atomic systems.