Genetic screens of the collection of ~4500 deletion mutants in Saccharomyces cerevisiae have identified the cohort of nonessential genes that promote maintenance of genome integrity. Here we probe the role of essential genes needed for genome stability. To this end, we screened 217 tetracycline-regulated promoter alleles of essential genes and identified 47 genes whose depletion results in spontaneous DNA damage. We further showed that 92 of these 217 essential genes have a role in suppressing chromosome rearrangements. We identified a core set of 15 genes involved in DNA replication that are critical in preventing both spontaneous DNA damage and genome rearrangements. Mapping, classification, and analysis of rearrangement breakpoints indicated that yeast fragile sites, Ty retrotransposons, tRNA genes, early origins of replication, and replication termination sites are common features at breakpoints when essential replication genes that suppress chromosome rearrangements are downregulated. We propose mechanisms by which depletion of essential replication proteins can lead to double-stranded DNA breaks near these features, which are subsequently repaired by homologous recombination at repeated elements.