Deep neural networks have become the method of choice for solving many classification tasks, largely because they can fit very complex functions defined over raw data. The downside of such powerful learners is the danger of overfit. In this paper, we introduce a novel ensemble classifier for deep networks that effectively overcomes overfitting by combining models generated at specific intermediate epochs during training. Our method allows for the incorporation of useful knowledge obtained by the models during the overfitting phase without deterioration of the general performance, which is usually missed when early stopping is used. To motivate this approach, we begin with the theoretical analysis of a regression model, whose prediction -- that the variance among classifiers increases when overfit occurs -- is demonstrated empirically in deep networks in common use. Guided by these results, we construct a new ensemble-based prediction method, where the prediction is determined by the class that attains the most consensual prediction throughout the training epochs. Using multiple image and text classification datasets, we show that when regular ensembles suffer from overfit, our method eliminates the harmful reduction in generalization due to overfit, and often even surpasses the performance obtained by early stopping. Our method is easy to implement and can be integrated with any training scheme and architecture, without additional prior knowledge beyond the training set. It is thus a practical and useful tool to overcome overfit. Code is available at https://github.com/uristern123/United-We-Stand-Using-Epoch-wise-Agreement-of-Ensembles-to-Combat-Overfit.