We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an environment, we derive a lower bound on the fidelity decay, which increases with increasing uncertainty in the state of the environment. Remarkably, this robustness in fidelity can be achieved even in fragile chaotic systems. We show that non-Markovianity is necessary for attaining robustness in the fidelity.