We report that the π-electrons of graphene can be spin-polarized to create a phase with a significant spin-orbit gap at the Dirac point (DP) using a graphene-interfaced topological insulator hybrid material. We have grown epitaxial Bi2Te2Se (BTS) films on a chemical vapor deposition (CVD) graphene. We observe two linear surface bands both from the CVD graphene notably flattened and BTS coexisting with their DPs separated by 0.53 eV in the photoemission data measured with synchrotron photons. We further demonstrate that the separation between the two DPs, ΔD-D, can be artificially fine-tuned by adjusting the amount of Cs atoms adsorbed on the graphene to a value as small as ΔD-D = 0.12 eV to find any proximity effect induced by the DPs. Our density functional theory calculation shows a spin-orbit gap of ~20 meV in the π-band enhanced by three orders of magnitude from that of a pristine graphene, and a concomitant phase transition from a semi-metallic to a quantum spin Hall phase when ΔD-D ≤ 0.20 eV. We thus present a practical means of spin-polarizing the π-band of graphene, which can be pivotal to advance the graphene-based spintronics.