During asymmetric division, fate determinants at the cell cortex segregate unequally into the two daughter cells. It has recently been shown that Sara (Smad anchor for receptor activation) signalling endosomes in the cytoplasm also segregate asymmetrically during asymmetric division. Biased dispatch of Sara endosomes mediates asymmetric Notch/Delta signalling during the asymmetric division of sensory organ precursors in Drosophila. In flies, this has been generalized to stem cells in the gut and the central nervous system, and, in zebrafish, to neural precursors of the spinal cord. However, the mechanism of asymmetric endosome segregation is not understood. Here we show that the plus-end kinesin motor Klp98A targets Sara endosomes to the central spindle, where they move bidirectionally on an antiparallel array of microtubules. The microtubule depolymerizing kinesin Klp10A and its antagonist Patronin generate central spindle asymmetry. This asymmetric spindle, in turn, polarizes endosome motility, ultimately causing asymmetric endosome dispatch into one daughter cell. We demonstrate this mechanism by inverting the polarity of the central spindle by polar targeting of Patronin using nanobodies (single-domain antibodies). This spindle inversion targets the endosomes to the wrong cell. Our data uncover the molecular and physical mechanism by which organelles localized away from the cellular cortex can be dispatched asymmetrically during asymmetric division.