Cyclin-dependent kinases (CDKs) drive major cell cycle events including the initiation of chromosomal DNA replication. We identified two S phase CDK (S-CDK) phosphorylation sites in the budding yeast Sld3 protein that, together, are essential for DNA replication. Here we show that, when phosphorylated, these sites bind to the amino-terminal BRCT repeats of Dpb11. An Sld3–Dpb11 fusion construct bypasses the requirement for both Sld3 phosphorylation and the N-terminal BRCT repeats of Dpb11. Co-expression of this fusion with a phospho-mimicking mutant in a second essential CDK substrate, Sld2, promotes DNA replication in the absence of S-CDK. Therefore, Sld2 and Sld3 are the minimal set of S-CDK targets required for DNA replication. DNA replication in cells lacking G1 phase CDK (G1-CDK) required expression of the Cdc7 kinase regulatory subunit, Dbf4, as well as Sld2 and Sld3 bypass. Our results help to explain how G1- and S-CDKs promote DNA replication in yeast.