Unsupervised domain adaptation (UDA) deals with the problem of classifying unlabeled target domain data while labeled data is only available for a different source domain. Unfortunately, commonly used classification methods cannot fulfill this task adequately due to the domain gap between the source and target data. In this paper, we propose a novel uncertainty-aware domain adaptation setup that models uncertainty as a multivariate Gaussian distribution in feature space. We show that our proposed uncertainty measure correlates with other common uncertainty quantifications and relates to smoothing the classifier's decision boundary, therefore improving the generalization capabilities. We evaluate our proposed pipeline on challenging UDA datasets and achieve state-of-the-art results. Code for our method is available at https://gitlab.com/tringwald/cvp.