Whole chromosome instability (W-CIN) is a hallmark of human cancer and contributes to the evolvement of aneuploidy. W-CIN can be induced by abnormally increased microtubule plus end assembly rates during mitosis leading to the generation of lagging chromosomes during anaphase as a major form of mitotic errors in human cancer cells. Here, we show that loss of the tumor suppressor genes TP53 and TP73 can trigger increased mitotic microtubule assembly rates, lagging chromosomes, and W-CIN. CDKN1A, encoding for the CDK inhibitor p21CIP1, represents a critical target gene of p53/p73. Loss of p21CIP1 unleashes CDK1 activity which causes W-CIN in otherwise chromosomally stable cancer cells. Consequently, induction of CDK1 is sufficient to induce abnormal microtubule assembly rates and W-CIN. Vice versa, partial inhibition of CDK1 activity in chromosomally unstable cancer cells corrects abnormal microtubule behavior and suppresses W-CIN. Thus, our study shows that the p53/p73 - p21CIP1 tumor suppressor axis, whose loss is associated with W-CIN in human cancer, safeguards against chromosome missegregation and aneuploidy by preventing abnormally increased CDK1 activity.