A universal feature of DNA damage and replication stress in eukaryotes is the activation of a checkpoint-kinase response. In S-phase, the checkpoint inhibits replication initiation, yet the function of this global block to origin firing remains unknown. To establish the physiological roles of this arm of the checkpoint, we analyzed separation of function mutants in the budding yeast Saccharomyces cerevisiae that allow global origin firing upon replication stress, despite an otherwise normal checkpoint response. Using genetic screens, we show that lack of the checkpoint-block to origin firing results in a dependence on pathways required for the resolution of topological problems. Failure to inhibit replication initiation indeed causes increased DNA catenation, resulting in DNA damage and chromosome loss. We further show that such topological stress is not only a consequence of a failed checkpoint response but also occurs in an unperturbed S-phase when too many origins fire simultaneously. Together we reveal that the role of limiting the number of replication initiation events is to prevent DNA topological problems, which may be relevant for the treatment of cancer with both topoisomerase and checkpoint inhibitors.