Cdk1 controls many aspects of mitotic chromosome behavior and spindle microtubule (MT) dynamics to ensure accurate chromosome segregation. In this paper, we characterize a new kinetochore substrate of fission yeast Cdk1, Nsk1, which promotes proper kinetochore-MT (k-MT) interactions and chromosome movements in a phosphoregulated manner. Cdk1 phosphorylation of Nsk1 antagonizes Nsk1 kinetochore and spindle localization during early mitosis. A nonphosphorylatable Nsk1 mutant binds prematurely to kinetochores and spindle, cementing improper k-MT attachments and leading to high rates of lagging chromosomes that missegregate. Accordingly, cells lacking nsk1 exhibit synthetic growth defects with mutations that disturb MT dynamics and/or kinetochore structure, and lack of proper phosphoregulation leads to even more severe defects. Intriguingly, Nsk1 is stabilized by binding directly to the dynein light chain Dlc1 independently of the dynein motor, and Nsk1-Dlc1 forms chainlike structures in vitro. Our findings establish new roles for Cdk1 and the Nsk1-Dlc1 complex in regulating the k-MT interface and chromosome segregation.