Cyclin-dependent kinase 1 (Cdk1) is absolutely essential for cell division. Complete ablation of Cdk1 precludes the entry of G2 phase cells into mitosis, and is early embryonic lethal in mice. Dampening Cdk1 activation, by reducing gene expression or upon treatment with cell-permeable Cdk1 inhibitors, is also detrimental for proliferating cells, but has been associated with defects in mitotic progression, and the formation of aneuploid daughter cells. Here, we used a large-scale RNAi screen to identify the human genes that critically determine the cellular toxicity of Cdk1 inhibition. We show that Cdk1 inhibition leads to fatal sister chromatid alignment errors and mitotic arrest in the spindle checkpoint. These problems start early in mitosis and are alleviated by depletion of isoform 1 of PRC1 (PRC1-1), by gene ablation of its binding partner KIF4, or by abrogation of KIF4 motor activity. Our results show that, normally, Cdk1 activity must rise above the level required for mitotic entry. This prevents KIF4-dependent PRC1-1 translocation to astral microtubule tips and safeguards proper chromosome congression. We conclude that cell death in response to Cdk1 inhibitors directly relates to chromosome alignment defects generated by insufficient repression of PRC1-1 and KIF4 during prometaphase.