  The ordering of the neutrino mass eigenstates is one of the fundamental open
questions in neutrino physics. While current-generation neutrino oscillation
experiments are able to produce moderate indications on this ordering, upcoming
experiments of the next generation aim to provide conclusive evidence. In this
paper we study the combined performance of the two future multi-purpose
neutrino oscillation experiments JUNO and the IceCube Upgrade, which employ two
very distinct and complementary routes towards the neutrino mass ordering. The
approach pursued by the $20\,\mathrm{kt}$ medium-baseline reactor neutrino
experiment JUNO consists of a careful investigation of the energy spectrum of
oscillated $\bar{\nu}_e$ produced by ten nuclear reactor cores. The IceCube
Upgrade, on the other hand, which consists of seven additional densely
instrumented strings deployed in the center of IceCube DeepCore, will observe
large numbers of atmospheric neutrinos that have undergone oscillations
affected by Earth matter. In a joint fit with both approaches, tension occurs
between their preferred mass-squared differences $ \Delta
m_{31}^{2}=m_{3}^{2}-m_{1}^{2} $ within the wrong mass ordering. In the case of
JUNO and the IceCube Upgrade, this allows to exclude the wrong ordering at
$>5\sigma$ on a timescale of 3--7 years --- even under circumstances that are
unfavorable to the experiments' individual sensitivities. For PINGU, a
26-string detector array designed as a potential low-energy extension to
IceCube, the inverted ordering could be excluded within 1.5 years (3 years for
the normal ordering) in a joint analysis.
