In the context of correlated insulators, where electron–electron interactions (U) drive the localization of charge carriers, the metal–insulator transition is described as either bandwidth- or filling-controlled1. Motivated by the challenge of the insulating phase in Sr2IrO4, a new class of correlated insulators has been proposed, in which spin–orbit coupling (SOC) is believed to renormalize the bandwidth of the half-filled jeff = 1/2 doublet, allowing a modest U to induce a charge-localized phase2,3. Although this framework has been tacitly assumed, a thorough characterization of the ground state has been elusive4,5. Furthermore, direct evidence for the role of SOC in stabilizing the insulating state has not been established, because previous attempts at revealing the role of SOC6,7 have been hindered by concurrently occurring changes to the filling8–10. We overcome this challenge by employing multiple substituents that introduce well-defined changes to the signatures of SOC and carrier concentration in the electronic structure, as well as a new methodology that allows us to monitor SOC directly. Specifically, we study Sr2Ir1−xTxO4 (T = Ru, Rh) by angle-resolved photoemission spectroscopy, combined with ab initio and supercell tight-binding calculations. This allows us to distinguish relativistic and filling effects, thereby establishing conclusively the central role of SOC in stabilizing the insulating state of Sr2IrO4. Most importantly, we estimate the critical value for SOC in this system to be λc = 0.42 ± 0.01 eV, and provide the first demonstration of a spin–orbit-controlled metal–insulator transition.