Cell-cycle checkpoints are essential feedback mechanisms that promote genome integrity. However, in the face of unrepairable DNA lesions, bypass mechanisms can suppress checkpoint activity and allow cells to resume proliferation. The molecular mechanisms underlying this biological response are currently not understood. Taking advantage of unique separation-of-function mutants, we show that the Polo-like kinase (PLK) Cdc5 uses a phosphopriming-based interaction mechanism to suppress G2/M checkpoint arrest by targeting Polo kinase activity to centrosomes. We also show that key subunits of the evolutionarily conserved RSC complex are critical downstream effectors of Cdc5 activity in checkpoint suppression. Importantly, the lethality and checkpoint defects associated with loss of Cdc5 Polo box activity can be fully rescued by artificially anchoring Cdc5 kinase domain to yeast centrosomes. Collectively, our results highlight a previously unappreciated role for centrosomes as key signaling centers for the suppression of cell-cycle arrest induced by persistent or unrepairable DNA damage.