Building upon the formulation of transverse-momentum resummation for heavy-quarkhadroproduction, we present the first application of theqTsubtraction formalism to thecomputation of electroweak corrections to massive lepton pairs through the Drell-Yanmechanism. We then study the power suppressed contributions to theqTsubtractionformula in the parameterrcut, defined as the minimum transverse momentum of thelepton pair normalised to its invariant mass. We analytically compute the leadingpower correction from initial and final-state radiation to the inclusive cross section.In the case of initial-state radiation the power correction isquadraticinrcutand ouranalytic result is consistent with results previously obtained in the literature. Final-state radiation produceslinearcontributions inrcutthat may challenge the efficiencyof theqTsubtraction procedure. We explicitly compute the linear power correction inthe case of the inclusive cross section and we discuss the extension of our calculationto differential distributions.