Context. Angular momentum loss through magnetic braking drives the spin-down of low-mass stars and the orbital evolution of a variety of close binary stars. Current theories for magnetic braking, often calibrated for one particular type of system, predict angular momentum loss rates that differ by several orders of magnitude. A unified prescription, even if fully empirical, would provide important constraints on the relation between angular momentum loss, stellar dynamos, and stellar magnetic activity. Aims. Recent studies have shown that a saturated, boosted, and disrupted (SBD) magnetic braking prescription explains the increase in the fraction of close systems among white dwarf plus M-dwarf binaries at the fully convective boundary, the period distribution of main-sequence star binaries, and the mass distribution of close M-dwarf companions to hot subdwarfs. With the aim of analyzing whether this prescription is also applicable to related binaries, we investigated the evolution of cataclysmic variables assuming a SBD magnetic braking prescription. Methods. We incorporated the SBD magnetic braking model into the stellar evolution code MESA and simulated the evolution of cataclysmic variables, testing different values for the boosting (K) and the disruption (eta) parameters for different stellar parameters. Results. The model accurately reproduces the mass transfer rates and the donor star mass-radius relation. The corresponding evolutionary tracks are in good agreement with the observed boundaries of the orbital period gap as well as the period minimum when assuming K similar or equal to eta similar or equal to 30 - 50. These values for K and eta are slightly smaller than but consistent with those determined from detached binaries (K similar or equal to eta greater than or similar to 50). Conclusions. Angular momentum loss through SBD magnetic braking can explain not only observations of detached binaries but also cataclysmic variables, that is, it is the only prescription currently available that is suitable for several types of close binary stars. The model needs to be tested further in the context of other close binary and single stars, and the currently used semi-empirical convective turnover time for main-sequence stars needs to be replaced with self-consistent turnover times.