We present a precision calculation of the transverse-momentum and invariant-mass distributions for supersymmetric particle pair production at hadron colliders, focusing on Drell-Yan like slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement the joint resummation formalism at the next-to-leading logarithmic accuracy with a process-independent Sudakov form factor, thus ensuring a universal description of soft-gluon emission, and consistently match the obtained result with the pure perturbative result at the first order in the strong coupling constant, i.e. at O(alpha_s). We also implement three different recent parameterizations of non-perturbative effects. Numerically, we give predictions for ~e_R ~e_R^* production and compare the resummed cross section with the perturbative result. The dependence on unphysical scales is found to be reduced, and non-perturbative contributions remain small.