Laws of corresponding states known so far demonstrate that certain macroscopic systems can be described in a universal manner in terms of reduced quantities, which eliminate specific substance properties. To quantitatively describe real systems, all these laws of corresponding states contain numerical factors adjusted empirically. Here, we report a law of corresponding states deduced analytically for charge transport via tunneling in molecular junctions, which we validate against current-voltage measurements for conducting probe atomic force microscope junctions based on benchmark molecular series (oligophenylenedithiols and alkanedithiols) and electrodes (silver, gold, and platinum), as well as against transport data for scanning tunneling microscope junctions. Two salient features distinguish the present law of corresponding states from all those known previously. First, it is expressed by a universal curve free of empirical parameters. Second, it demonstrates that a universal behavior is not necessarily affected by strong stochastic fluctuations often observed in molecular electronics. An important and encouraging message of this finding is that transport behavior across different molecular platforms can be similar and extraordinarily reproducible.