Spin-orbit entanglement in 4d and 5d transition metal systems can enhance electronic correlations, leading to nontrivial ground states and the emergence of exotic excitations. There is also an interest to investigate spin-orbit entanglement in 3d compounds, though this is challenging due to their smaller spin-orbit coupling. Here we demonstrate that the Jahn-Teller effect in Mn3+ reduces the energy gap between high- and low- spin-orbital states that lead to enhanced spin-orbit entanglement. Our results show a rare example of synergistic effects of Jahn-Teller and spin-orbit interactions and provide a way to entangle different degrees of freedom in d-metal oxides, which may allow paths to explore the interplay of orbital, lattice and spins in 3d correlated systems.