We demonstrate a detailed procedure to resum threshold-enhanced logarithms to all orders in perturbative QCD in the rapidity distribution of a system of non-QCD partons produced at the hadron colliders. The resummation procedure has been carried out in the double-Mellin space where the kinematics get factorized. As an immediate application of our formalism, we consider both Higgs boson production and a pair of leptons through Drell-Yan at the LHC to next-to-next-to-leading logarithmic accuracy matched to the corresponding fixed order results. We find that inclusion of these threshold logarithms through resummation procedure improves the reliability of perturbative predictions.