An analysis is presented based on models of the intrinsic transverse momentum (intrinsic $k_\mathrm{T}$) of partons in nucleons by studying the dilepton transverse momentum in Drell-Yan events. Using parameter tuning in event generators and existing data from fixed-target experiments and from hadron colliders, our investigation spans three orders of magnitude in center-of-mass energy and two orders of magnitude in dilepton invariant mass. The results show an energy-scaling behavior of the intrinsic $k_\mathrm{T}$ parameters, independent of the dilepton invariant mass at a given center-of-mass energy.