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Under global change, the impact of seed banks on evolutionary rescue is uncertain. They buffer plant populations from demographic and genetic stochasticity but extend generation time and can become a reservoir of maladapted alleles. We built analytical and individual-based models to predict the effect of seed banks on the persistence of small annual plant populations facing an abrupt or sustained directional change in uni- or multivariate trait optima. Demogenetic dynamics predict that under most scenarios seed banks increase the lag yet enhance persistence to 200–250 years by absorbing demographic losses. Simulations indicate that the seed bank has a minimal impact on the genetic skew, although we suggest that this result could depend on the fitness component under selection. Our multivariate model reveals that by enlarging and reshaping the G matrix, seed banks can diminish the impact of mutational correlation and even accelerate adaptation under antagonistic pleiotropy relative to populations without a bank. We illustrate how the magnitude of optimum fluctuations, type and degree of optimum change, selection strength, and vital rates are weights that tip the scales determining persistence. Finally, our work highlights that migration from the past is not maladaptative when optimum fluctuations are large enough to create stepping stones to the new optimum.