Bloom's syndrome is caused by inactivation of the BLM helicase, which functions with TOP3A and RMI1-2 (BTR complex) to dissolve recombination intermediates and avoid somatic crossing-over. We show here that crossover avoidance by BTR further requires the activity of cyclin-dependent kinase-1 (CDK1), Polo-like kinase-1 (PLK1), and the DDR mediator protein TOPBP1, which act in the same pathway. Mechanistically, CDK1 phosphorylates BLM and TOPBP1 and promotes the interaction of both proteins with PLK1. This is amplified by the ability of TOPBP1 to facilitate phosphorylation of BLM at sites that stimulate both BLM-PLK1 and BLM-TOPBP1 binding, creating a positive feedback loop that drives rapid BLM phosphorylation at the G2-M transition. In vitro, BLM phosphorylation by CDK/PLK1/TOPBP1 stimulates the dissolution of topologically linked DNA intermediates by BLM-TOP3A. Thus, we propose that the CDK1-TOPBP1-PLK1 axis enhances BTR-mediated dissolution of recombination intermediates late in the cell cycle to suppress crossover recombination and curtail genomic instability.