The ages of young star clusters are fundamental clocks to constrain the formation and evolution of pre-main-sequence stars and their protoplanetary disks and exoplanets. However, dating methods for very young clusters often disagree, casting doubts on the accuracy of the derived ages. We propose a new method to derive the kinematic age of star clusters based on the evaporation ages of their stars. The method was validated and calibrated using hundreds of clusters identified in a supernova-driven simulation of the interstellar medium forming stars for approximately 40Myr within a 250pc region. We demonstrate that the clusters' evaporation-age uncertainty can be as small as about 10% for clusters with a large enough number of evaporated stars and small but with realistic observational errors. We have obtained evaporation ages for a pilot sample of ten clusters, finding a good agreement with their published isochronal ages. The evaporation ages will provide important constraints for modeling the pre-main-sequence evolution of low-mass stars, as well as allow for the star formation and gas-evaporation history of young clusters to be investigated. These ages can be more accurate than isochronal ages for very young clusters, for which observations and models are more uncertain.