We analyze magnetic field profiles of vortices in thin-film superconductors, shedding new light on this old and presumed settled problem. In sufficiently thin films with realistic Ginzburg-Landau parameter, $\kappa =1/\sqrt{2}$, the magnetic screening around a vortex core does not follow the exponential decay expected in bulk, nor do we recover the power-law behavior predicted by Pearl. Our results complement Pearl’s description in this realistic regime, where finite vortex-core effects prevent access to the asymptotic Pearl behaviors. Instead, we find a universal function describing the field variation, whose amplitude is set by the film thickness. This thickness dependence is consistent with the seminal Pearl length, and serves as an indication of the reduced field screening present in two-dimensional superconductors. Finally, we quantify the crossover from bulk-like to thin-film superconductors, and establish different screening length scales relevant for the analysis of experimental data.