The critical rate of catalytic surface reactions leading to gas-phase ignition in non-premixed stagnation-point flows over a porous plate is investigated theoretically. The relationships between the critical rate of catalytic surface reactions at ignition and the temperature of fuel mixture supplied from the lower side of the porous plate exhibit a C-shaped ignition curve and a near-linear ignition profile for small and great injected mass fluxes, respectively. Physically, the upper and the lower branches of C-shaped ignition curves are governed by the diffusionally and the kinetically controlled ignition, respectively. The entire near-linear ignition profiles are diffusionally controlled. The diffusionally controlled ignition mechanisms for the upper branch of C-shaped ignition curves and the near-linear ignition profiles are caused by rapid catalytic reactions and great injected mass fluxes, respectively. Two characteristic ignition temperatures, i.e., the critical ignition temperature and the minimum ignition temperature, as functions of various system parameters are identified and analyzed. The transition between the kinetically and the diffusionally controlled ignition is investigated. In addition, influences of the injected mass flux, the strain rate of flow, the Prandtl number and the Schmidt number on the C-shaped ignition curve and the near-linear ignition profile are systematically discussed.