We propose a method of adapting pretrained depth completion models to test time data in an unsupervised manner. Depth completion models are (pre)trained to produce dense depth maps from pairs of RGB image and sparse depth maps in ideal capture conditions (source domain), e.g., well-illuminated, high signal-to-noise. When models are transferred to capture conditions out of ideal case (target domain), they produce erroneous output dense depth maps due to the covariate shift. To identify cases of out-of-distribution errors, we propose an learn an energy model in the source domain that assigns scalars that represent the likelihood of the output dense depth maps. This energy model is further used to adapt the pretrained depth completion models at test time, leading to our method: Energy-based Test-time Adaptation (ETA). ETA can localize regions of errors as high energy; test-time adaptation involves updating the model weights to minimize the energy, which in turn mitigates the covariate shift. We evaluate ETA across 3 indoor and 3 outdoor datasets, where ETA improves over the previous state of the art by an average of 6.94% on outdoor and 10.23% on indoor settings.