We identify a new universality in the carrier transport of two-dimensional (2D) material-based Schottky heterostructures. We show that the reversed saturation current (J) scales universally with temperature (T) as log(J/T^{β})∝-1/T, with β=3/2 for lateral Schottky heterostructures and β=1 for vertical Schottky heterostructures, over a wide range of 2D systems including nonrelativistic electron gas, Rashba spintronic systems, single- and few-layer graphene, transition metal dichalcogenides, and thin films of topological solids. Such universalities originate from the strong coupling between the thermionic process and the in-plane carrier dynamics. Our model resolves some of the conflicting results from prior works and is in agreement with recent experiments. The universal scaling laws signal the breakdown of β=2 scaling in the classic diode equation widely used over the past sixty years. Our findings shall provide a simple analytical scaling for the extraction of the Schottky barrier height in 2D material-based heterostructures, thus paving the way for both a fundamental understanding of nanoscale interface physics and applied device engineering.