  We consider Drell-Yan production $pp \to Z/\gamma^* \to \ell^+\ell^-$ with
the simultaneous measurement of the $Z$-boson transverse momentum $q_T$ and
$0$-jettiness $\mathcal{T}_0$. Since both observables resolve the initial-state
QCD radiation, the double-differential cross section in $q_T$ and
$\mathcal{T}_0$ contains Sudakov double logarithms of both $q_T/Q$ and
$\mathcal{T}_0/Q$, where $Q \sim m_Z$ is the dilepton invariant mass. We
simultaneously resum the logarithms in $q_T$ and $\mathcal{T}_0$ to
next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading
fixed order (NLO). Our results provide the first genuinely two-dimensional
analytic Sudakov resummation for initial-state radiation. Integrating the
resummed double-differential spectrum with an appropriate scale choice over
either $\mathcal{T}_0$ or $q_T$ recovers the corresponding single-differential
resummation for the remaining variable. We discuss in detail the required
effective field theory setups and their combination using two-dimensional
resummation profile scales. We also introduce a new method to perform the $q_T$
resummation where the underlying resummation is carried out in impact-parameter
space, but is consistently turned off depending on the momentum-space target
value for $q_T$. Our methods apply at any order and for any color-singlet
production process, such that our results can be systematically extended when
the relevant perturbative ingredients become available.
