The interplay between superconductivity and charge or spin order is a key focus in condensed matter physics, with kagome lattice systems providing unique insights. The kagome superconductor LaRu₃Si₂ (T_c≃ 6.5 K) features a characteristic kagome band structure and a hierarchy of charge order transitions at T_co,I≃ 400 K and T_co,II≃ 80 K, along with an additional transition at T* ≃ 35 K associated with electronic and magnetic responses. Using magnetotransport under pressure up to 40 GPa, we find T_c peaks at 9 K (2 GPa)—the highest among kagome superconductors—remains nearly constant up to 12 GPa, and then decreases to 2 K at 40 GPa, forming a dome-shaped phase diagram. Similarly, both the resistivity anomaly at T* and the magnetoresistance exhibit a dome-shaped pressure dependence. Moreover, above 12 GPa, X-ray diffraction reveals that the charge order evolves from long-range to short-range, coinciding with the suppression of T_c. These observations indicate that superconductivity in LaRu₃Si₂ is closely linked to the charge-ordered state and the electronic responses at T_co,II and T*.