Cyclin-dependent kinases (CDKs) lie at the heart of eukaryotic cell cycle control, with different cyclin–CDK complexes initiating DNA replication (S-CDKs) and mitosis (M-CDKs)1,2. However, the principles on which cyclin–CDK complexes organize the temporal order of cell cycle events are contentious3. One model proposes that S-CDKs and M-CDKs are functionally specialized, with substantially different substrate specificities to execute different cell cycle events4–6. A second model proposes that S-CDKs and M-CDKs are redundant with each other, with both acting as sources of overall CDK activity7,8. In this model, increasing CDK activity, rather than CDK substrate specificity, orders cell cycle events9,10. Here we reconcile these two views of core cell cycle control. Using phosphoproteomic assays of in vivo CDK activity in fission yeast, we find that S-CDK and M-CDK substrate specificities are remarkably similar, showing that S-CDKs and M-CDKs are not completely specialized for S phase and mitosis alone. Normally, S-CDK cannot drive mitosis but can do so when protein phosphatase 1 is removed from the centrosome. Thus, increasing S-CDK activity in vivo is sufficient to overcome substrate specificity differences between S-CDK and M-CDK, and allows S-CDK to carry out M-CDK function. Therefore, we unite the two opposing views of cell cycle control, showing that the core cell cycle engine is largely based on a quantitative increase in CDK activity through the cell cycle, combined with minor and surmountable qualitative differences in catalytic specialization of S-CDKs and M-CDKs.