We present a novel approach for the simultaneous determination of the thermal conductivity κ and the total interface conductance g of supported 2D materials by the enhanced opto-thermal method. We harness the property of the Gaussian laser beam that acts as a heat source, whose size can easily and precisely be controlled. The experimental data for multi-layer graphene and MoS₂ flakes are supplemented using numerical simulations of the heat distribution in the Si/SiO2/2D material system. The procedure of κ and g extraction is tested in a statistical approach, demonstrating the high accuracy and repeatability of our method.