Coherent interactions between excitons strongly coupled to plasmons are vital for quantum information devices. For practical applications, suppressing the incoherent dissipation pathways in the hybrid system is essential. Here, we report on a strong plasmon-exciton coupling in a monolayer WS₂/graphene van der Waals heterostructure (WS₂/Gr vdWhs) integrated with an Au nanocube (Au NC). The presence of graphene effectively suppresses the non-radiative decay pathway of neutral excitons in the vdWhs, resulting in a narrower photoluminescence (PL) linewidth. The further integration of the WS₂/Gr vdWhs with the Au NC enables coherent interaction between the in-plane exciton and a tilted plasmonic dipole, delivering a Rabi splitting energy of 120 meV and an incoherent coupling strength of 1 meV. Our findings possess the potential to facilitate the advancement of quantum nanophotonic devices.