  We report on the first complete computation of the mixed QCD$-$electroweak
(EW) corrections to the neutral-current Drell$-$Yan process. Superseding
previously applied approximations, our calculation provides the first result at
this order that is valid in the entire range of dilepton invariant masses. The
two-loop virtual contribution is computed by using semi-analytical techniques,
overcoming the technical problems in the evaluation of the relevant master
integrals. The cancellation of soft and collinear singularities is achieved by
a formulation of the $q_T$ subtraction formalism valid in presence of charged
massive particles in the final state. We present numerical results for the
fiducial cross section and selected kinematical distributions. At large values
of the lepton $p_T$ the mixed QCD$-$EW corrections are negative and increase in
size, to about $-15\%$ with respect to the next-to-leading-order QCD result at
$p_T=500\,$GeV. Up to dilepton invariant masses of 1 TeV the computed
corrections amount to about $-1.5\%$ with respect to the next-to-leading-order
QCD result.
