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Adversarial examples induce model classification errors on purpose, which has raised concerns on the security aspect of machine learning techniques. Many existing countermeasures are compromised by adaptive adversaries and transferred examples. We propose a model-agnostic approach to resolve the problem by analysing the model responses to an input under random perturbations, and study the robustness of detecting norm-bounded adversarial distortions in a theoretical framework. Extensive evaluations are performed on the MNIST, CIFAR-10 and ImageNet datasets. The results demonstrate that our detection method is effective and resilient against various attacks including black-box attacks and the powerful CW attack with four adversarial adaptations.