The two centrosomes present at the onset of mitosis must separate in a timely and accurate fashion to ensure proper bipolar spindle assembly. The minus-end-directed motor dynein plays a pivotal role in centrosome separation, but the underlying mechanisms remain elusive, particularly regarding how dynein coordinates this process in space and time. We addressed these questions in the one-cell C. elegans embryo, using a combination of 3D timelapse microscopy and computational modeling. Our analysis reveals that centrosome separation is powered by the joint action of dynein at the nuclear envelope and at the cell cortex. Strikingly, we demonstrate that dynein at the cell cortex acts as a force-transmitting device that harnesses polarized actomyosin cortical flows initiated by the centrosomes earlier in the cell cycle. This mechanism elegantly couples cell polarization with centrosome separation, thus ensuring faithful cell division.