We propose a simple, statistically principled, and theoretically justified method to improve supervised learning when the training set is not representative, a situation known as covariate shift. We build upon a well-established methodology in causal inference and show that the effects of covariate shift can be reduced or eliminated by conditioning on propensity scores. In practice, this is achieved by fitting learners within strata constructed by partitioning the data based on the estimated propensity scores, leading to approximately balanced covariates and much-improved target prediction. We refer to the overall method as Stratified Learning, or StratLearn. We demonstrate the effectiveness of this general-purpose method on two contemporary research questions in cosmology, outperforming state-of-the-art importance weighting methods. We obtain the best-reported AUC (0.958) on the updated “Supernovae photometric classification challenge,” and we improve upon existing conditional density estimation of galaxy redshift from Sloan Digital Sky Survey (SDSS) data.