© 2020 authors. Published by the American Physical Society. 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 toward the neutrino mass ordering. The approach pursued by the 20 kt medium-baseline reactor neutrino experiment JUNO consists of a careful investigation of the energy spectrum of oscillated νe 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 Δm312=m32-m12 within the wrong mass ordering. In the case of JUNO and the IceCube Upgrade, this allows to exclude the wrong ordering at >5σ 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.