The charge injection barriers in organic field-effect transistors (OFETs) seem to be far less critical as compared to organic light-emitting diodes (OLEDs). Counter intuitively; we show that the origin is image-force lowering of the barrier due to the gate bias at the source contact; although the corresponding gate field is perpendicular to the channel current. In coplanar OFETs; injection barriers up to 1 eV can be surmounted by increasing the gate bias; enabling extraction of bulk transport parameters in this regime. For staggered transistors; however; the injection is gate-assisted only until the gate bias is screened by the accumulation channel opposite to the source contact. The gate-assisted injection is supported by two-dimensional numerical charge transport simulations that reproduce the gate-bias dependence of the contact resistance and the typical S-shaped output curves as observed for OFETs with high injection barriers.