Quasi-two-dimensional perovskites have emerged as a new material platform for optoelectronics on account of its intrinsic stability. A major bottleneck to device performance is the high charge injection barrier caused by organic molecular layers on its basal plane, thus the best performing device currently relies on edge contact. Herein, by leveraging on van der Waals coupling and energy level matching between two-dimensional Ruddlesden-Popper perovskite and graphene, we show that the plane-contacted perovskite and graphene interface presents a lower barrier than gold for charge injection. Electron tunneling across the interface occurs via a gate-tunable, direct tunneling-to-field emission mechanism with increasing bias, and photoinduced charge transfer occurs at femtosecond timescale (~50 fs). Field effect transistors fabricated on molecularly thin Ruddlesden-Popper perovskite using graphene contact exhibit electron mobilities ranging from 0.1 to 0.018 cm²V⁻¹s⁻¹ between 1.7 to 200 K. Scanning tunneling spectroscopy studies reveal layer-dependent tunneling barrier and domain size on few-layered Ruddlesden-Popper perovskite.