Deep neural networks have achieved remarkable success in a variety of computer vision applications. However, there is a problem of degrading accuracy when the data distribution shifts between training and testing. As a solution of this problem, Test-time Adaptation~(TTA) has been well studied because of its practicality. Although TTA methods increase accuracy under distribution shift by updating the model at test time, using high-uncertainty predictions is known to degrade accuracy. Since the input image is the root of the distribution shift, we incorporate a new perspective on enhancing the input image into TTA methods to reduce the prediction's uncertainty. We hypothesize that enhancing the input image reduces prediction's uncertainty and increase the accuracy of TTA methods. On the basis of our hypothesis, we propose a novel method: Test-time Enhancer and Classifier Adaptation~(TECA). In TECA, the classification model is combined with the image enhancement model that transforms input images into recognition-friendly ones, and these models are updated by existing TTA methods. Furthermore, we found that the prediction from the enhanced image does not always have lower uncertainty than the prediction from the original image. Thus, we propose logit switching, which compares the uncertainty measure of these predictions and outputs the lower one. In our experiments, we evaluate TECA with various TTA methods and show that TECA reduces prediction's uncertainty and increases accuracy of TTA methods despite having no hyperparameters and little parameter overhead.